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 adiabatic limit procedure associates with every solution of Abelian Higgs model in （2 ^- 1） dimensions a geodesic in the moduli space of static solutions. We show that the same procedure for Seiberg- Witten equa...The adiabatic limit procedure associates with every solution of Abelian Higgs model in （2 ^- 1） dimensions a geodesic in the moduli space of static solutions. We show that the same procedure for Seiberg- Witten equations on 4-dimensional symplectic manifolds introduced by Taubes may be considered as a complex （2＋2）-dimensional version of the （2＋ 1）-dimensional picture. More precisely, the adiabatic limit procedure in the 4-dimensional case associates with a solution of Seiberg-Witten equations a pseudoholomorphic divisor which may be treated as a complex version of a geodesic in （2＋l）-dimensional case.展开更多
In this paper,Seiberg-Witten-like equations w让hout self-duality are defined on any smooth 2n+1-dimensional Spinc manifolds.Then,a non-trivial solution is given on the strictly-Pseudoconvex CR-5 manifolds endowed with...In this paper,Seiberg-Witten-like equations w让hout self-duality are defined on any smooth 2n+1-dimensional Spinc manifolds.Then,a non-trivial solution is given on the strictly-Pseudoconvex CR-5 manifolds endowed with a canonical Spincstructure by using Dirac operator associated with the generalized Tanaka-Webster connection.Finally,some bounds are given to them on the 5-dimensional Riemannian manifolds.展开更多
We give an analogy of Seiberg-Witten monopole equations on flat Euclidian space R5. For this we used an irreducible representation of complex Clifford algebra Cl5. For the curvature equation we use a kind of self-dual...We give an analogy of Seiberg-Witten monopole equations on flat Euclidian space R5. For this we used an irreducible representation of complex Clifford algebra Cl5. For the curvature equation we use a kind of self-duality notion of a 2-form on R5 which is given in [1].展开更多
Following the approach of our previous paper we continue to study the asymptotic solution of periodic Schrodinger operators. Using the eigenvalues obtained earlier the corresponding asymptotic wave functions are deriv...Following the approach of our previous paper we continue to study the asymptotic solution of periodic Schrodinger operators. Using the eigenvalues obtained earlier the corresponding asymptotic wave functions are derived. This gives further evidence in favor of the monodromy relations for the Floquet exponent proposed in the previous paper. In particular, the large energy asymptotic wave functions are related to the instanton partition function of N = 2 supersymmetric gauge theory with surface operator. A relevant number theoretic dessert is appended.展开更多
We study the problem of how the Floquet property manifests for periodic Schr6dinger operators,which axe known to have multiple of asymptotic spectral solutions.The main conclusions are made for elliptic potentials,we ...We study the problem of how the Floquet property manifests for periodic Schr6dinger operators,which axe known to have multiple of asymptotic spectral solutions.The main conclusions are made for elliptic potentials,we demonstrate that for each period of the elliptic function there is a relation about the Floquet exponent and the monodromy of wave function.Among them there are two relations not explained by the classical Floquet theory.These relations produce both old and new asymptotic solutions consistent with results already known.展开更多
We investigate the decomposition of noncommutative gauge potential Ai, and find that it has inner structure, namely, Ai can be decomposed in two parts, bi and αi, where bi satisfies gauge transformations while αi sa...We investigate the decomposition of noncommutative gauge potential Ai, and find that it has inner structure, namely, Ai can be decomposed in two parts, bi and αi, where bi satisfies gauge transformations while αi satisfies adjoint transformations, so dose the Seiberg-Witten mapping of noncommutative U（1） gauge potential. By means of Seiberg-Witten mapping, we construct a mapping of unit vector field between noncommutative space and ordinary space, and find the noncommutative U（1） gauge potential and its gauge field tensor can be expressed in terms of the unit vector field. When the unit vector field has no singularity point, noncommutative gauge potential and gauge field tensor will equal ordinary gauge potential and gauge field tensor展开更多
In N = 2 super Yang-Mills theory, the Matone＇s relation relates instanton corrections of the prepotential to instanton corrections of scMar field condensation （Trφ2）. This relation has been proved to hold for Omeg...In N = 2 super Yang-Mills theory, the Matone＇s relation relates instanton corrections of the prepotential to instanton corrections of scMar field condensation （Trφ2）. This relation has been proved to hold for Omega deformed theories too, using localization method. In this paper, we first give a case study supporting the relation, which does not rely on the localization technique. Especially, we show that the magnetic expansion also satisfies a relation of Matone＇s type. Then we discuss implication of the relation for proposed Nekrasov-Shatashvili scheme. the spectrum of periodic Toda chain, in the context of recentlyproposed Nekrasov-Shatashvili scheme.展开更多
In this paper we research the lower bound of the eigenvalue of Spinc Dirac operator on the Spinc manifold. By the Weisenbock formula, we get an estimate of it, then following the idea of Th Friedrich [2] and X Zhang [...In this paper we research the lower bound of the eigenvalue of Spinc Dirac operator on the Spinc manifold. By the Weisenbock formula, we get an estimate of it, then following the idea of Th Friedrich [2] and X Zhang [6]. We get a finer estimate of it. As an application, we give a condition when the Seiberg-Witten equation only has 0 solution.展开更多
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.
基金supported by Russian Foundation of Basic Research(Grants Nos.16-01-00117 and 16-52-12012)the Program of support of Leading Scientific Schools(Grants No.NSh-9110.2016.1)the Program of Presidium of Russian Academy of Sciences“Nonlinear dynamics”
文摘The adiabatic limit procedure associates with every solution of Abelian Higgs model in （2 ^- 1） dimensions a geodesic in the moduli space of static solutions. We show that the same procedure for Seiberg- Witten equations on 4-dimensional symplectic manifolds introduced by Taubes may be considered as a complex （2＋2）-dimensional version of the （2＋ 1）-dimensional picture. More precisely, the adiabatic limit procedure in the 4-dimensional case associates with a solution of Seiberg-Witten equations a pseudoholomorphic divisor which may be treated as a complex version of a geodesic in （2＋l）-dimensional case.
文摘In this paper,Seiberg-Witten-like equations w让hout self-duality are defined on any smooth 2n+1-dimensional Spinc manifolds.Then,a non-trivial solution is given on the strictly-Pseudoconvex CR-5 manifolds endowed with a canonical Spincstructure by using Dirac operator associated with the generalized Tanaka-Webster connection.Finally,some bounds are given to them on the 5-dimensional Riemannian manifolds.
文摘We give an analogy of Seiberg-Witten monopole equations on flat Euclidian space R5. For this we used an irreducible representation of complex Clifford algebra Cl5. For the curvature equation we use a kind of self-duality notion of a 2-form on R5 which is given in [1].
基金supported by the FAPESP No.2011/21812-8,through IFT-UNESP
文摘Following the approach of our previous paper we continue to study the asymptotic solution of periodic Schrodinger operators. Using the eigenvalues obtained earlier the corresponding asymptotic wave functions are derived. This gives further evidence in favor of the monodromy relations for the Floquet exponent proposed in the previous paper. In particular, the large energy asymptotic wave functions are related to the instanton partition function of N = 2 supersymmetric gauge theory with surface operator. A relevant number theoretic dessert is appended.
文摘We study the problem of how the Floquet property manifests for periodic Schr6dinger operators,which axe known to have multiple of asymptotic spectral solutions.The main conclusions are made for elliptic potentials,we demonstrate that for each period of the elliptic function there is a relation about the Floquet exponent and the monodromy of wave function.Among them there are two relations not explained by the classical Floquet theory.These relations produce both old and new asymptotic solutions consistent with results already known.
基金the Talent Introduction Project of Xianyang Normal University under Grant No.07XSYK217
文摘We investigate the decomposition of noncommutative gauge potential Ai, and find that it has inner structure, namely, Ai can be decomposed in two parts, bi and αi, where bi satisfies gauge transformations while αi satisfies adjoint transformations, so dose the Seiberg-Witten mapping of noncommutative U（1） gauge potential. By means of Seiberg-Witten mapping, we construct a mapping of unit vector field between noncommutative space and ordinary space, and find the noncommutative U（1） gauge potential and its gauge field tensor can be expressed in terms of the unit vector field. When the unit vector field has no singularity point, noncommutative gauge potential and gauge field tensor will equal ordinary gauge potential and gauge field tensor
基金Supported by the Natural Science Foundation of China under Grant No.11031005
文摘In N = 2 super Yang-Mills theory, the Matone＇s relation relates instanton corrections of the prepotential to instanton corrections of scMar field condensation （Trφ2）. This relation has been proved to hold for Omega deformed theories too, using localization method. In this paper, we first give a case study supporting the relation, which does not rely on the localization technique. Especially, we show that the magnetic expansion also satisfies a relation of Matone＇s type. Then we discuss implication of the relation for proposed Nekrasov-Shatashvili scheme. the spectrum of periodic Toda chain, in the context of recentlyproposed Nekrasov-Shatashvili scheme.
基金Supported in part by Mathematics Tianyuan Fund(10226002)
文摘In this paper we research the lower bound of the eigenvalue of Spinc Dirac operator on the Spinc manifold. By the Weisenbock formula, we get an estimate of it, then following the idea of Th Friedrich [2] and X Zhang [6]. We get a finer estimate of it. As an application, we give a condition when the Seiberg-Witten equation only has 0 solution.
