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

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 ${\text{F}}_{ikl}{\beta }^{lm}{\text{F}}_{mnj}={\text{F}}_{jkl}{\beta }^{lm}{\text{F}}_{mni}$. The conjecture that the WDVV--like equations are equivalent to the identity involving the $u$--modulus and the prepotential $\text{F}$, seen as a superconformal anomaly, sheds light on the recently considered c-theorem for the N=2 SYM field theories.

Comments: 6 pages, LaTeX, References added