Comments on Bounds on Central Charges in N=1 Superconformal Theories

TL;DR

This paper investigates the bounds on the ratio of central charges in N=1 superconformal theories, confirming the proposed limits through calculations on specific interacting models and noting saturation by free theories.

Contribution

It provides explicit computations of the central charge ratio for certain N=1 SCFTs, supporting the proposed bounds and clarifying their applicability to interacting theories.

Findings

No violations of the bounds were found in the studied models.

The bounds are saturated by free field theories.

The results support the conjectured limits on central charge ratios.

Abstract

The ratio of central charges in four-dimensional CFTs has been suggested by Hofman and Maldacena to lie within an interval whose boundaries are fixed by the number of supersymmetries. We compute this ratio for a set of interacting N=1 superconformal field theories which arise as RG fixed points of supersymmetric Yang-Mills theories with adjoint and fundamental matter. We do not find violations of the proposed bounds, which appear to be saturated by free field theories.