RG Flow Irreversibility, C-Theorem and Topological Nature of 4D N=2 SYM

TL;DR

This paper derives an exact RG flow potential for 4D N=2 SYM, revealing a topological structure and proposing a 4D analogue of the c-theorem based on the classical discriminants of Seiberg-Witten curves.

Contribution

It introduces a novel RG potential for N=2 SYM derived from Seiberg-Witten curves and formulates a 4D c-theorem analogue, highlighting the topological aspects of the theory.

Findings

RG flow is irreversible in SU(2) case

RG potential relates to classical discriminants of Seiberg-Witten curves

Evidence of topological nature of N=2 SYM

Abstract

We determine the exact beta function and a RG flow Lyapunov function for N=2 SYM with gauge group SU(n). It turns out that the classical discriminants of the Seiberg-Witten curves determine the RG potential. The radial irreversibility of the RG flow in the SU(2) case and the non-perturbative identity relating the $u$-modulus and the superconformal anomaly, indicate the existence of a four dimensional analogue of the c-theorem for N=2 SYM which we formulate for the full SU(n) theory. Our investigation provides further evidence of the essentially topological nature of the theory.