Dual WDVV Equations in N=2 Supersymmetric Yang-Mills Theory

Abstract

This paper studies the dual form of Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equations in N=2 supersymmetric Yang-Mills theory by applying a duality transformation to WDVV equations. The dual WDVV equations called in this paper are non-linear differential equations satisfied by dual prepotential and are found to have the same form with the original WDVV equations. However, in contrast with the case of weak coupling calculus, the perturbative part of dual prepotential itself does not satisfy the dual WDVV equations. Nevertheless, it is possible to show that the non-perturbative part of dual prepotential can be determined from dual WDVV equations, provided the perturbative part is given. As an example, the SU(4) case is presented. The non-perturbative dual prepotential derived in this way is consistent to the dual prepotential obtained by D'Hoker and Phong.

misprints are corrected, revtex, 10 pages

References in corpus (4)

• Seiberg-Witten theory for a non-trivial compactification from five to four dimensions
• Instanton Recursion Relations for the Effective Prepotential in N=2 Super Yang-Mills
• Seiberg-Witten Theory as d<1 Topological Strings
• Differential Equations for Scaling Relation in N=2 Supersymmetric SU(2) Yang-Mills Theory Coupled with Massive Hypermultiplet

Cited by in corpus (5)

• The Dijkgraaf-Vafa prepotential in the context of general Seiberg-Witten theory
• DV and WDVV
• Experiments with the WDVV equations for the gluino-condensate prepotential: the cubic (two-cut) case
• Electric-Magnetic Duality and WDVV Equations
• Duality Transformations for Generalized WDVV equations in Seiberg-Witten theory