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

TL;DR

This paper provides a straightforward proof of the WDVV equations for the prepotential in four-dimensional N=2 supersymmetric Yang-Mills theory, linking them to two-dimensional topological models and exploring their broader implications.

Contribution

It offers a simple proof of the WDVV equations for all ADE gauge groups and extends the analysis to BC groups within the Landau-Ginzburg framework, highlighting their topological origins.

Findings

WDVV equations originate from associativity in 2D topological Landau-Ginzburg models

Proof applies to all ADE gauge groups in N=2 Yang-Mills theory

Explores Landau-Ginzburg framework for BC gauge groups

Abstract

We present a simple proof of the WDVV equations for the prepotential of four-dimensional N=2 supersymmetric Yang-Mills theory with all ADE gauge groups. According to our proof it is clearly seen that the WDVV equations in four dimensions have their origin in the associativity of the chiral ring in two-dimensional topological Landau-Ginzburg models. The WDVV equations for the BC gauge groups are also studied in the Landau-Ginzburg framework. We speculate about the topological field theoretic interpretation of the Seiberg-Witten solution of N=2 Yang-Mills theory.