Associativity Equations in Effective SUSY Quantum Field Theories

TL;DR

This paper explores the role of associativity (WDVV) equations in effective supersymmetric quantum field theories, showing how their solutions relate to residue formulas, duality, and integrable systems.

Contribution

It demonstrates that for many solutions, associativity equations can be proven via linear equations, highlighting their covariance under duality and connection to integrable systems.

Findings

Associativity equations can be reduced to linear systems under certain conditions.

Residue formulas are crucial for the validity of solutions.

Associativity equations are covariant under duality transformations.

Abstract

The role of associativity or WDVV equations in effective supersymmetric quantum theories is discussed and it is demonstrated that for wide class of their solutions when residue formulas are valid the proof of associativity equations can be reduced to solving the system of ordinary linear equations and depends only upon corresponding matching and nondegeneracy conditions. The covariance of WDVV equations upon generic duality transformations and the role of associativity equations in general context of quasiclassical integrable systems is also discussed.