Central charges of N=2 superconformal field theories in four dimensions

TL;DR

This paper introduces a method to compute the central charges a and c of N=2 superconformal field theories by analyzing U(1)_R anomalies, and applies it to various gauge theories, confirming previous results and deriving new bounds.

Contribution

It provides a general anomaly-based method for calculating central charges in N=2 SCFTs and establishes bounds on the ratio a/c.

Findings

Calculated a and c for multiple gauge theories including N=4 SU(N) and USp(2N).

Reproduced known conformal and flavor central charges from gravity duals.

Proved bounds on the ratio a/c between 1/2 and 5/4.

Abstract

We present a general method for computing the central charges a and c of N=2 superconformal field theories corresponding to singular points in the moduli space of N=2 gauge theories. Our method relates a and c to the U(1)_R anomalies of the topologically twisted gauge theory. We evaluate these anomalies by studying the holomorphic dependence of the path integral measure on the moduli. We calculate a and c for superconformal points in a variety of gauge theories, including N=4 SU(N), N=2 pure SU(N) Yang-Mills, and USp(2N) with 1 massless antisymmetric and 4 massive fundamental hypermultiplets. In the latter case, we reproduce the conformal and flavor central charges previously calculated using the gravity duals of these gauge theories. For any SCFT in the class under consideration, we derive a previously conjectured expression for 2a-c in terms of the sum of the dimensions of operators parameterizing the Coulomb branch. Finally, we prove that the ratio a/c is bounded above by 5/4 and below by 1/2.