In this manuscript,a reduced(3+1)-dimensional nonlinear evolution equation is studied.We first construct the bilinear formalism of the equation by using the binary Bell polynomials theory,then explore a lump solution ...In this manuscript,a reduced(3+1)-dimensional nonlinear evolution equation is studied.We first construct the bilinear formalism of the equation by using the binary Bell polynomials theory,then explore a lump solution to the special case for z=x.Furthermore,a more general form of lump solution of the equation is found which possesses seven arbitrary parameters and four constraint conditions.By cutting the lump by the induced soliton(s),lumpoff and instanton/rogue wave solutions are also constructed by the more general form of lump solution.展开更多
The mass spectrum of the S-wave mesons is considered in the frame work of relativistic harmonic model （RHM）. The full Hamiltonian used in the investigation has the Lorentz scalar plus a vector harmonic-oscillator po...The mass spectrum of the S-wave mesons is considered in the frame work of relativistic harmonic model （RHM）. The full Hamiltonian used in the investigation has the Lorentz scalar plus a vector harmonic-oscillator potential, the confined-one-gluon-exchange potential （COGEP） and the instanton-induced quark-antiquak interaction （Ⅲ）. A good description of the mass spectrum is obtained. The respective role of Ⅲ and COGEP in the S-wave meson spectrum is discussed.展开更多
The instanton induced cross section in deep inelastic kinematics is a subject which people are tendentious to investigate it. Instanton induced contributions are well defined for the nucleon structure function. The no...The instanton induced cross section in deep inelastic kinematics is a subject which people are tendentious to investigate it. Instanton induced contributions are well defined for the nucleon structure function. The non-perturbative contribution to the quark distributions of structure function, F2（x, Q2）, is considered within an instanton model for the QCD vacuum. We find that the structure function may possess numerically large non-perterbative contributions which are related to the violation of chirality and correspond to the correction of parton distribution of the leading twist. It is shown that the instantons give a negative contribution to the structure function at the NLO approximation. A comparison between our results, considering instantaon effect, and the case when we do not take this effect is done. Taking into account the instanton size, p, via the modified running coupling constant we get to a good agreement between our results at the NLO and NNLO approximations and the available experimental data, specially at the low values of the Bjorken variable x 〈 0.1 which confirms the validity of our calculations.展开更多
Gluon propagator is investigated for pure Yang-Mills SU(3) gauge theory in field-strength approach. It isfound that instantohs provide a homogeneous solid-like medium background which generates finite nonzero momentum...Gluon propagator is investigated for pure Yang-Mills SU(3) gauge theory in field-strength approach. It isfound that instantohs provide a homogeneous solid-like medium background which generates finite nonzero momentumgluon propagator and gluon receives effective mass.展开更多
There are two distinct phases in the evolution of drift wave envelope in the presence of zonal flow.A long-lived standing wave phase,which we call the Caviton,and a short-lived traveling wave phase(in radial direction...There are two distinct phases in the evolution of drift wave envelope in the presence of zonal flow.A long-lived standing wave phase,which we call the Caviton,and a short-lived traveling wave phase(in radial direction) we call the Instanton.Several abrupt phenomena observed in tokamaks,such as intermittent excitation of geodesic acoustic mode(GAM) shown in this paper,could be attributed to the sudden and fast radial motion of Instanton.The composite drift wave-zonal flow system evolves at the two well-separate scales:the micro-scale and the meso-scale.The eigenmode equation of the model defines the zero-order(micro-scale) variation;it is solved by making use of the two-dimensional(2 D) weakly asymmetric ballooning theory(WABT),a theory suitable for modes localized to rational surface like drift waves,and then refined by shifted inverse power method,an iterative finite difference method.The next order is the equation of electron drift wave(EDW) envelope(containing group velocity of EDW) which is modulated by the zonal flow generated by Reynolds stress of EDW.This equation is coupled to the zonal flow equation,and numerically solved in spatiotemporal representation;the results are displayed in self-explanatory graphs.One observes a strong correlation between the Caviton-Instanton transition and the zero-crossing of radial group velocity of EDW.The calculation brings out the defining characteristics of the Instanton:it begins as a linear traveling wave right after the transition.Then,it evolves to a nonlinear stage with increasing frequency all the way to 20 kHz.The modulation to Reynolds stress in zonal flow equation brought in by the nonlinear Instanton will cause resonant excitation to GAM.The intermittency is shown due to the random phase mixing between multiple central rational surfaces in the reaction region.展开更多
In this article, we study the pentaquark state Θ＋（1540） with a （scalar） diquark-（pseudoscalar） diquarkantiquark type interpolating current in the framework of the QCD sum rules approach by including the contri...In this article, we study the pentaquark state Θ＋（1540） with a （scalar） diquark-（pseudoscalar） diquarkantiquark type interpolating current in the framework of the QCD sum rules approach by including the contributions from the direct instantons. The numerical results indicate that the contributions from the direct instantons are very small and can be safely neglected.展开更多
We obtain the instanton correction recursion relations for the low energy effective prepotential in pure Ν = 2SU(n) supersymmetric Yang-Mills gauge theory from Whitham hierarchy and Seiberg-Witten/Whitham equations. ...We obtain the instanton correction recursion relations for the low energy effective prepotential in pure Ν = 2SU(n) supersymmetric Yang-Mills gauge theory from Whitham hierarchy and Seiberg-Witten/Whitham equations. These formulae provide us a powerful tool to calculate arbitrary order instanton corrections coefficients from the perturbative contributions of the effective prepotential in Seiberg-Witten gauge theory. We apply this idea to evaluate one-and two-order instanton corrections coefficients explicitly in SU(n) case in detail through the dynamical scale parameter expressed in terms of Riemann's theta-function.展开更多
The mass spectrum of the D wave mesons is considered in the frame work of relativistic harmonic model (RHM). The full Hamiltonian used in the investigation has the Lorentz scalar plus a vector harmonic-oscillator pote...The mass spectrum of the D wave mesons is considered in the frame work of relativistic harmonic model (RHM). The full Hamiltonian used in the investigation has the Lorentz scalar plus a vector harmonic-oscillator potential, the confined-one-gluon-exchange potential (COGEP) and the instanton-induced quark-antiquark interaction (III). A good agreement between calculated D wave meson masses with experimental D wave meson masses is obtained. The respective role of III and COGEP in the D wave meson spectrum is discussed.展开更多
Under condition of four potential fields, equations of motion and fluctuations in imaginary time are utilized to analytically derive the basic and fluctuating periodic instantons. It is shown that the basic instantons...Under condition of four potential fields, equations of motion and fluctuations in imaginary time are utilized to analytically derive the basic and fluctuating periodic instantons. It is shown that the basic instantons satisfy the elliptic or simple pendulum equations and their solutions are Jacobi elliptic functions, and fluctuating periodic instantons satisfy the Lam′e equation and their solutions are Lame functions. These results indicate that there exists the common solution family for different potential fields which are called the super-symmetry family.展开更多
Employing a 4-form ansatz of 11-dimensional supergravity over a non-dynamical AdS_(4)×S^(7)/Z_(k)background and setting the internal space as an S1 Hopf fibration on CP3,we obtain a consistent truncation.The(pseu...Employing a 4-form ansatz of 11-dimensional supergravity over a non-dynamical AdS_(4)×S^(7)/Z_(k)background and setting the internal space as an S1 Hopf fibration on CP3,we obtain a consistent truncation.The(pseudo)scalars,in the resulting scalar equations in Euclidean AdS_(4)space,may be considered to arise from(anti)M-branes wrapping around the internal directions in the(Wick-rotated)skew-whiffed M2-brane background(as the resulting theory is for anti-M2-branes),thus realizing the modes after swapping the three fundamental representations 8_(s),8_(c),and 8_(v) of SO(8).Taking the backreaction on the external and internal spaces,we obtain the massless and massive modes,corresponding to exactly marginal and marginally irrelevant deformations on the boundary CFT3,respectively.Subsequently,we obtain a closed solution for the bulk equation and compute its correction with respect to the background action.Next,considering the Higgs-like(breathing)mode m^(2)=18,having all supersymmetries as well as parity and scale-invariance broken,solving the associated bulk equation with mathematical methods,specifically the Adomian decomposition method,and analyzing the behavior near the boundary of the solutions,we realize the boundary duals in the SU(4)×U(1)-singlet sectors of the ABJM model.Then,introducing the new dual deformationΔ_(+)=3,6 operators made of bi-fundamental scalars,fermions,and U(1)gauge fields,we obtain the SO(4)-invariant solutions as small instantons on a three-sphere with the radius at infinity,which correspond to collapsing bulk bubbles leading to big-crunch singularities.展开更多
A gravitational instanton is considered as the seed for the creation of a universe. However, there exist too few instantons. To include many interesting phenomena in the framework of quantum cosmology, the concept of ...A gravitational instanton is considered as the seed for the creation of a universe. However, there exist too few instantons. To include many interesting phenomena in the framework of quantum cosmology, the concept of constrained gravitational instanton is inevitable. In this paper we show how a primordial black hole is created from a constrained instanton. The quantum creation of a generic black hole in the closed or open background is completely resolved. The relation of the creation scenario with gravitational thermodynamics and topology is discussed.展开更多
The scaling and additivity properties of Rényi entropy in rapidity space of the instanton final state （IFS） and current jet identified by the r-sorting method from the QCDINS Monte Carlo event sample are studie...The scaling and additivity properties of Rényi entropy in rapidity space of the instanton final state （IFS） and current jet identified by the r-sorting method from the QCDINS Monte Carlo event sample are studied. Asymptotic scaling of the Rényi entropy H2 is observed for the IFS while H2 for the current jet jtends to saturation with decreasing phase space scale. Furthermore, it is found that the additivity of H2 holds well for the IFS in narrow rapidity windows at different positions. These results indicate that the IFS produced in the instanton-induced process of deep inelastic scattering has reached local equilibrium.展开更多
We discuss possible implications of exotic stringy instantons for baryon-violating signatures in future colliders. In particular, we discuss high-energy quark collisions and A- transitions. In principle, the A-A proce...We discuss possible implications of exotic stringy instantons for baryon-violating signatures in future colliders. In particular, we discuss high-energy quark collisions and A- transitions. In principle, the A-A process can be probed by high-luminosity electron-positron colliders. However, we find that an extremely high luminosity is needed in order to provide a （somewhat） stringent bound compared to the current data on NN→ππ,KK. On the other hand, （exotic） instanton-induced six-quark interactions can be tested in near future high-energy colliders beyond LHC, at energies around 20-100 TeV. The Super proton-proton Collider （SppC） would be capable of such measurement given the proposed energy level of 50-90 TeV. Comparison with other channels is made. In particular, we show the compatibility of our model with neutron-antineutron and NN→ππ, KK bounds.展开更多
The bubble tree compactified instanton moduli space -Mκ （X） is introduced. Its singularity set Singκ（X） is described. By the standard gluing theory, one can show that- Mκ（X） - Singκ（X） is a topological orb...The bubble tree compactified instanton moduli space -Mκ （X） is introduced. Its singularity set Singκ（X） is described. By the standard gluing theory, one can show that- Mκ（X） - Singκ（X） is a topological orbifold. In this paper, we give an argument to construct smooth structures on it.展开更多
The Drinfeld-Manin construction of U（N） instanton is reformulated in the ADHM formulism, which gives explicit general solutions of the ADHM constraints for U（N） （N ≥ 2k - 1） k-instantons. For the N 〈 2k - 1 ca...The Drinfeld-Manin construction of U（N） instanton is reformulated in the ADHM formulism, which gives explicit general solutions of the ADHM constraints for U（N） （N ≥ 2k - 1） k-instantons. For the N 〈 2k - 1 case, implicit results are given systematically as further constraints. We find that this formulism can easily be generalized to the noncommutative case, where the explicit solutions are also obtained.展开更多
We discuss the Atiyah-Drinfeld-Hitchin-Manin （ADHM） construc- tion of U（N） instantons in noncommutative （NC） space and give some exact instanton solutions for various noncommutative settings. We also present a n...We discuss the Atiyah-Drinfeld-Hitchin-Manin （ADHM） construc- tion of U（N） instantons in noncommutative （NC） space and give some exact instanton solutions for various noncommutative settings. We also present a new formula which is crucial to show an origin of the instanton number for U（1） and to prove the one-to-one correspondence between moduli spaces of the noncommutative instantons and the ADHM data.展开更多
We investigate instanton effects on the heavy-quark potential, including its spin-dependent part, based on the instanton liquid model. Starting with the central potential derived from the instanton vacuum, we obtain t...We investigate instanton effects on the heavy-quark potential, including its spin-dependent part, based on the instanton liquid model. Starting with the central potential derived from the instanton vacuum, we obtain the spin-dependent part of the heavy-quark potential. We discuss the results of the heavy-quark potential from the instanton vacuum. Finally, we solve the nonrelativistic two-body problem, associated with the heavy-quark potential from the instanton vacuum. The instanton effects on the quarkonia spectra are marginal but are required for quantitative description of the spectra.展开更多
Considering the importance of higher-dimensional equations that are widely applied to real nonlinear problems,many(4+1)-dimensional integrable systems have been established by uplifting the dimensions of their corresp...Considering the importance of higher-dimensional equations that are widely applied to real nonlinear problems,many(4+1)-dimensional integrable systems have been established by uplifting the dimensions of their corresponding lower-dimensional integrable equations.Recently,an integrable(4+1)-dimensional extension of the Boiti-Leon-Manna-Pempinelli(4DBLMP)equation has been proposed,which can also be considered as an extension of the famous Korteweg-de Vries equation that is applicable in fluids,plasma physics and so on.It is shown that new higher-dimensional variable separation solutions with several arbitrary lowerdimensional functions can also be obtained using the multilinear variable separation approach for the 4DBLMP equation.In addition,by taking advantage of the explicit expressions of the new solutions,versatile(4+1)-dimensional nonlinear wave excitations can be designed.As an illustration,periodic breathing lumps,multi-dromion-ring-type instantons,and hybrid waves on a doubly periodic wave background are discovered to reveal abundant nonlinear structures and dynamics in higher dimensions.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11675084 and 11435005)the Fund from the Educational Commission of Zhejiang Province,China(Grant No.Y201737177)+1 种基金Ningbo Natural Science Foundation(Grant No.2015A610159)the K C Wong Magna Fund in Ningbo University
文摘In this manuscript,a reduced(3+1)-dimensional nonlinear evolution equation is studied.We first construct the bilinear formalism of the equation by using the binary Bell polynomials theory,then explore a lump solution to the special case for z=x.Furthermore,a more general form of lump solution of the equation is found which possesses seven arbitrary parameters and four constraint conditions.By cutting the lump by the induced soliton(s),lumpoff and instanton/rogue wave solutions are also constructed by the more general form of lump solution.
基金the DST for funding the project (Sanction No.SR/S2/HEP-14/2006)
文摘The mass spectrum of the S-wave mesons is considered in the frame work of relativistic harmonic model （RHM）. The full Hamiltonian used in the investigation has the Lorentz scalar plus a vector harmonic-oscillator potential, the confined-one-gluon-exchange potential （COGEP） and the instanton-induced quark-antiquak interaction （Ⅲ）. A good description of the mass spectrum is obtained. The respective role of Ⅲ and COGEP in the S-wave meson spectrum is discussed.
文摘The instanton induced cross section in deep inelastic kinematics is a subject which people are tendentious to investigate it. Instanton induced contributions are well defined for the nucleon structure function. The non-perturbative contribution to the quark distributions of structure function, F2（x, Q2）, is considered within an instanton model for the QCD vacuum. We find that the structure function may possess numerically large non-perterbative contributions which are related to the violation of chirality and correspond to the correction of parton distribution of the leading twist. It is shown that the instantons give a negative contribution to the structure function at the NLO approximation. A comparison between our results, considering instantaon effect, and the case when we do not take this effect is done. Taking into account the instanton size, p, via the modified running coupling constant we get to a good agreement between our results at the NLO and NNLO approximations and the available experimental data, specially at the low values of the Bjorken variable x 〈 0.1 which confirms the validity of our calculations.
文摘Gluon propagator is investigated for pure Yang-Mills SU(3) gauge theory in field-strength approach. It isfound that instantohs provide a homogeneous solid-like medium background which generates finite nonzero momentumgluon propagator and gluon receives effective mass.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.U1967206,11975231,11805203,and 11775222)the National MCF Energy Research and Development Program,China(Grant Nos.2018YFE0311200 and 2017YFE0301204)the Key Research Program of Frontier Sciences,Chinese Academy of Sciences(Grant No.QYZDB-SSW-SYS004)。
文摘There are two distinct phases in the evolution of drift wave envelope in the presence of zonal flow.A long-lived standing wave phase,which we call the Caviton,and a short-lived traveling wave phase(in radial direction) we call the Instanton.Several abrupt phenomena observed in tokamaks,such as intermittent excitation of geodesic acoustic mode(GAM) shown in this paper,could be attributed to the sudden and fast radial motion of Instanton.The composite drift wave-zonal flow system evolves at the two well-separate scales:the micro-scale and the meso-scale.The eigenmode equation of the model defines the zero-order(micro-scale) variation;it is solved by making use of the two-dimensional(2 D) weakly asymmetric ballooning theory(WABT),a theory suitable for modes localized to rational surface like drift waves,and then refined by shifted inverse power method,an iterative finite difference method.The next order is the equation of electron drift wave(EDW) envelope(containing group velocity of EDW) which is modulated by the zonal flow generated by Reynolds stress of EDW.This equation is coupled to the zonal flow equation,and numerically solved in spatiotemporal representation;the results are displayed in self-explanatory graphs.One observes a strong correlation between the Caviton-Instanton transition and the zero-crossing of radial group velocity of EDW.The calculation brings out the defining characteristics of the Instanton:it begins as a linear traveling wave right after the transition.Then,it evolves to a nonlinear stage with increasing frequency all the way to 20 kHz.The modulation to Reynolds stress in zonal flow equation brought in by the nonlinear Instanton will cause resonant excitation to GAM.The intermittency is shown due to the random phase mixing between multiple central rational surfaces in the reaction region.
基金The project supported by National Natural Science Foundation of China under Grant No. 10405009 and the Key Program Foundation of North China Electric Power University
文摘In this article, we study the pentaquark state Θ＋（1540） with a （scalar） diquark-（pseudoscalar） diquarkantiquark type interpolating current in the framework of the QCD sum rules approach by including the contributions from the direct instantons. The numerical results indicate that the contributions from the direct instantons are very small and can be safely neglected.
基金Supported by the National Natural Science Foundation of China under Grant No.11271079
文摘We obtain the instanton correction recursion relations for the low energy effective prepotential in pure Ν = 2SU(n) supersymmetric Yang-Mills gauge theory from Whitham hierarchy and Seiberg-Witten/Whitham equations. These formulae provide us a powerful tool to calculate arbitrary order instanton corrections coefficients from the perturbative contributions of the effective prepotential in Seiberg-Witten gauge theory. We apply this idea to evaluate one-and two-order instanton corrections coefficients explicitly in SU(n) case in detail through the dynamical scale parameter expressed in terms of Riemann's theta-function.
文摘The mass spectrum of the D wave mesons is considered in the frame work of relativistic harmonic model (RHM). The full Hamiltonian used in the investigation has the Lorentz scalar plus a vector harmonic-oscillator potential, the confined-one-gluon-exchange potential (COGEP) and the instanton-induced quark-antiquark interaction (III). A good agreement between calculated D wave meson masses with experimental D wave meson masses is obtained. The respective role of III and COGEP in the D wave meson spectrum is discussed.
基金Supportted by the National Natural Science Foundation of China under Grant No.40975027
文摘Under condition of four potential fields, equations of motion and fluctuations in imaginary time are utilized to analytically derive the basic and fluctuating periodic instantons. It is shown that the basic instantons satisfy the elliptic or simple pendulum equations and their solutions are Jacobi elliptic functions, and fluctuating periodic instantons satisfy the Lam′e equation and their solutions are Lame functions. These results indicate that there exists the common solution family for different potential fields which are called the super-symmetry family.
文摘Employing a 4-form ansatz of 11-dimensional supergravity over a non-dynamical AdS_(4)×S^(7)/Z_(k)background and setting the internal space as an S1 Hopf fibration on CP3,we obtain a consistent truncation.The(pseudo)scalars,in the resulting scalar equations in Euclidean AdS_(4)space,may be considered to arise from(anti)M-branes wrapping around the internal directions in the(Wick-rotated)skew-whiffed M2-brane background(as the resulting theory is for anti-M2-branes),thus realizing the modes after swapping the three fundamental representations 8_(s),8_(c),and 8_(v) of SO(8).Taking the backreaction on the external and internal spaces,we obtain the massless and massive modes,corresponding to exactly marginal and marginally irrelevant deformations on the boundary CFT3,respectively.Subsequently,we obtain a closed solution for the bulk equation and compute its correction with respect to the background action.Next,considering the Higgs-like(breathing)mode m^(2)=18,having all supersymmetries as well as parity and scale-invariance broken,solving the associated bulk equation with mathematical methods,specifically the Adomian decomposition method,and analyzing the behavior near the boundary of the solutions,we realize the boundary duals in the SU(4)×U(1)-singlet sectors of the ABJM model.Then,introducing the new dual deformationΔ_(+)=3,6 operators made of bi-fundamental scalars,fermions,and U(1)gauge fields,we obtain the SO(4)-invariant solutions as small instantons on a three-sphere with the radius at infinity,which correspond to collapsing bulk bubbles leading to big-crunch singularities.
文摘A gravitational instanton is considered as the seed for the creation of a universe. However, there exist too few instantons. To include many interesting phenomena in the framework of quantum cosmology, the concept of constrained gravitational instanton is inevitable. In this paper we show how a primordial black hole is created from a constrained instanton. The quantum creation of a generic black hole in the closed or open background is completely resolved. The relation of the creation scenario with gravitational thermodynamics and topology is discussed.
基金Supported by NSFC-RFBR Cooperative Research Project(10475030,05-02-39028-NNSF-a)NSFC(10375025,90503001)Ministry of Education of China NO CFKSTIP-704035
文摘The scaling and additivity properties of Rényi entropy in rapidity space of the instanton final state （IFS） and current jet identified by the r-sorting method from the QCDINS Monte Carlo event sample are studied. Asymptotic scaling of the Rényi entropy H2 is observed for the IFS while H2 for the current jet jtends to saturation with decreasing phase space scale. Furthermore, it is found that the additivity of H2 holds well for the IFS in narrow rapidity windows at different positions. These results indicate that the IFS produced in the instanton-induced process of deep inelastic scattering has reached local equilibrium.
基金supported in part by the MIUR research grant “Theoretical Astroparticle Physics” PRIN 2012CPPYP7partly supported by the DFG and the NSFC through funds provided to the Sino-German CRC 110 “Symmetries and the Emergence of Structure in QCD”+2 种基金MOST,Taiwan,(104-2112-M-001-022)from April 2017Supported by MEPhI Academic Excellence Project(contract 02.03.21.0005,27.08.2013)supported by the Ministry of Education and Science of Russian Federation,project 3.472.2014/K and grant RFBR 14-22-03048
文摘We discuss possible implications of exotic stringy instantons for baryon-violating signatures in future colliders. In particular, we discuss high-energy quark collisions and A- transitions. In principle, the A-A process can be probed by high-luminosity electron-positron colliders. However, we find that an extremely high luminosity is needed in order to provide a （somewhat） stringent bound compared to the current data on NN→ππ,KK. On the other hand, （exotic） instanton-induced six-quark interactions can be tested in near future high-energy colliders beyond LHC, at energies around 20-100 TeV. The Super proton-proton Collider （SppC） would be capable of such measurement given the proposed energy level of 50-90 TeV. Comparison with other channels is made. In particular, we show the compatibility of our model with neutron-antineutron and NN→ππ, KK bounds.
基金Supported by NSF Key Project 10631050A0109a 973 project 2006CB805900
文摘The bubble tree compactified instanton moduli space -Mκ （X） is introduced. Its singularity set Singκ（X） is described. By the standard gluing theory, one can show that- Mκ（X） - Singκ（X） is a topological orbifold. In this paper, we give an argument to construct smooth structures on it.
基金Supported by National Natural Science Foundation of China (10605005)President Fund of GUCAS
文摘The Drinfeld-Manin construction of U（N） instanton is reformulated in the ADHM formulism, which gives explicit general solutions of the ADHM constraints for U（N） （N ≥ 2k - 1） k-instantons. For the N 〈 2k - 1 case, implicit results are given systematically as further constraints. We find that this formulism can easily be generalized to the noncommutative case, where the explicit solutions are also obtained.
文摘We discuss the Atiyah-Drinfeld-Hitchin-Manin （ADHM） construc- tion of U（N） instantons in noncommutative （NC） space and give some exact instanton solutions for various noncommutative settings. We also present a new formula which is crucial to show an origin of the instanton number for U（1） and to prove the one-to-one correspondence between moduli spaces of the noncommutative instantons and the ADHM data.
基金Supported by Basic Science Research Program through the National Research Foundation(NRF)of Korea funded by the Korean government(Ministry of Education,Science and Technology,MEST)Grant Numbers 2016R1D1A1B03935053(UY)and 2015R1D1A1A01060707(HChK)partly Supported by RIKEN iTHES Project
文摘We investigate instanton effects on the heavy-quark potential, including its spin-dependent part, based on the instanton liquid model. Starting with the central potential derived from the instanton vacuum, we obtain the spin-dependent part of the heavy-quark potential. We discuss the results of the heavy-quark potential from the instanton vacuum. Finally, we solve the nonrelativistic two-body problem, associated with the heavy-quark potential from the instanton vacuum. The instanton effects on the quarkonia spectra are marginal but are required for quantitative description of the spectra.
基金supported by the National Natural Science Foundation of China (Grant Nos.12275085 and 12235007)the Science and Technology Commission of Shanghai Municipality (Grant No.22DZ2229014)。
文摘Considering the importance of higher-dimensional equations that are widely applied to real nonlinear problems,many(4+1)-dimensional integrable systems have been established by uplifting the dimensions of their corresponding lower-dimensional integrable equations.Recently,an integrable(4+1)-dimensional extension of the Boiti-Leon-Manna-Pempinelli(4DBLMP)equation has been proposed,which can also be considered as an extension of the famous Korteweg-de Vries equation that is applicable in fluids,plasma physics and so on.It is shown that new higher-dimensional variable separation solutions with several arbitrary lowerdimensional functions can also be obtained using the multilinear variable separation approach for the 4DBLMP equation.In addition,by taking advantage of the explicit expressions of the new solutions,versatile(4+1)-dimensional nonlinear wave excitations can be designed.As an illustration,periodic breathing lumps,multi-dromion-ring-type instantons,and hybrid waves on a doubly periodic wave background are discovered to reveal abundant nonlinear structures and dynamics in higher dimensions.
