Whitham Deformations of Seiberg-Witten Curves for Classical Gauge Groups

Abstract

Gorsky et al. presented an explicit construction of Whitham deformations of the Seiberg-Witten curve for the $SU(N+1)$ $\calN = 2$ SUSY Yang-Mills theory. We extend their result to all classical gauge groups and some other cases such as the spectral curve of the $A_{2N}^{(2)}$ affine Toda Toda system. Our construction, too, uses fractional powers of the superpotential $W(x)$ that characterizes the curve. We also consider the $u$-plane integral of topologically twisted theories on four-dimensional manifolds $X$ with $b_2^{+}(X)=1$ in the language of these explicitly constructed Whitham deformations and an integrable hierarchy of the KdV type hidden behind.

latex, 39pp, no figure; some more comments and references on integrable systems are added, and many typos are corrected

References in corpus (8)

• Issues in Topological Gauge Theory
• RG Equations from Whitham Hierarchy
• Testing Seiberg-Witten Solution
• Integrating over the Coulomb branch in N=2 gauge theory
• Integrable Hierarchies and Contact Terms in u-plane Integrals of Topologically Twisted Supersymmetric Gauge Theories
• Flat Coordinates, Topological Landau-Ginzburg Models and the Seiberg-Witten Period Integrals
• N=2 SYM RG Scale as Modulus for WDVV Equations
• Seiberg-Witten Theory as d<1 Topological Strings

Cited by in corpus (4)

• N=2 supersymmetric gauge theories with massive hypermultiplets and the Whitham hierarchy
• Blowup Equations for Refined Topological Strings
• The Lax pairs for elliptic C_n and BC_n Ruijsenaars-Schneider models and their spectral curves
• Blowup formulae in Donaldson-Witten theory and integrable hierarchies