Beta Function, C--Theorem and WDVV Equations in 4D N=2 SYM

TL;DR

This paper explores the relationship between the beta function, WDVV equations, and superconformal anomalies in 4D N=2 supersymmetric Yang-Mills theories, providing insights into their mathematical structure and c-theorem implications.

Contribution

It demonstrates that the inverse of the exact beta function satisfies WDVV-like equations and links these to superconformal anomalies in N=2 SYM.

Findings

Beta function acts as a metric satisfying WDVV-like equations.

WVVV equations relate to superconformal anomalies and the u-modulus.

Insights into the c-theorem for N=2 SYM theories.

Abstract

We show that the exact $beta$--function of 4D N=2 SYM plays the role of the metric whose inverse satisfies the WDVV--like equations $\F_{ikl}\beta^{lm} \F_{mnj}=\F_{jkl}\beta^{lm}\F_{mni}$. The conjecture that the WDVV--like equations are equivalent to the identity involving the $u$--modulus and the prepotential $\F$, seen as a superconformal anomaly, sheds light on the recently considered c-theorem for the N=2 SYM field theories.