WDVV Equations as Functional Relations

TL;DR

This paper shows that WDVV equations, which encode associativity in topological field theories, can be reformulated as functional relations between second derivatives of a single function, akin to dispersionless Hirota equations.

Contribution

It introduces a novel functional relation framework for WDVV equations, providing new insights into their structure and properties.

Findings

Reformulation of WDVV equations as functional relations

Comparison with dispersionless Hirota equations

Discussion of properties of these functional relations

Abstract

We discuss the associativity or WDVV equations and demonstrate that they can be rewritten as certain functional relations between the {\it second} derivatives of a single function, similar to the dispersionless Hirota equations. The properties of these functional relations are further discussed.