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

TL;DR

This paper explores the dual form of WDVV equations in N=2 supersymmetric Yang-Mills theory, revealing their structure, limitations in perturbative solutions, and the determination of non-perturbative dual prepotentials, exemplified by SU(4).

Contribution

It introduces dual WDVV equations in N=2 SYM, analyzes their properties, and demonstrates how to derive non-perturbative dual prepotentials from them.

Findings

Dual WDVV equations have the same form as original equations.

Perturbative dual prepotential does not satisfy dual WDVV equations.

Non-perturbative dual prepotential can be determined from dual WDVV equations.

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.