Generalized WDVV equations for B_r and C_r pure N=2 Super-Yang-Mills theory

TL;DR

This paper proves that the prepotential in pure N=2 Super-Yang-Mills theories for Lie algebras B_r and C_r satisfies the generalized WDVV equations, confirming the algebraic structure of holomorphic differentials.

Contribution

It explicitly demonstrates that certain objects used in previous approaches are indeed the structure constants of the algebra of holomorphic differentials.

Findings

Confirmed the algebraic structure of holomorphic differentials in the theory.

Validated the generalized WDVV equations for B_r and C_r Lie algebras.

Clarified the nature of objects used in alternative approaches.

Abstract

A proof that the prepotential for pure N=2 Super-Yang-Mills theory associated with Lie algebras B_r and C_r satisfies the generalized WDVV (Witten-Dijkgraaf-Verlinde-Verlinde) system was given by Marshakov, Mironov and Morozov. Among other things, they use an associative algebra of holomorphic differentials. Later Ito and Yang used a different approach to try to accomplish the same result, but they encountered objects of which it is unclear whether they form structure constants of an associative algebra. We show by explicit calculation that these objects are none other than the structure constants of the algebra of holomorphic differentials.