标题： 变形的N=2理论，广义递归关系和S对偶性 显示英文标题

标题： Deformed N=2 theories, generalized recursion relations and S-duality

摘要： 我们使用局部化技术研究四维N=2超共形场论的非微扰性质。 特别是我们考虑由通用epsilon背景变形的SU(2)规范理论，具有四个基本味或一个伴随超多重态。 在这两种情况下，我们使用Nekrasov的方法显式计算了配分函数和预势的前几项瞬子修正。 这些结果允许重构涉及裸规范耦合常数的准模函数的精确表达式，并表明预势项满足一个模异常方程，该方程的形式为带有显式epsilon依赖项的递归关系。 随后，我们研究了这种递归关系对有效理论模性质的影响，并发现通过适当重新定义预势和有效耦合，在至少变形参数的第三阶范围内，可以将S对偶关系写成与未变形理论的Seiberg-Witten解中出现的形式相同。 显示英文摘要

摘要： We study the non-perturbative properties of N=2 super conformal field theories in four dimensions using localization techniques. In particular we consider SU(2) gauge theories, deformed by a generic epsilon-background, with four fundamental flavors or with one adjoint hypermultiplet. In both cases we explicitly compute the first few instanton corrections to the partition function and the prepotential using Nekrasov's approach. These results allow to reconstruct exact expressions involving quasi-modular functions of the bare gauge coupling constant and to show that the prepotential terms satisfy a modular anomaly equation that takes the form of a recursion relation with an explicitly epsilon-dependent term. We then investigate the implications of this recursion relation on the modular properties of the effective theory and find that with a suitable redefinition of the prepotential and of the effective coupling it is possible, at least up to the third order in the deformation parameters, to cast the S-duality relations in the same form as they appear in the Seiberg-Witten solution of the undeformed theory.