Bounds on Triangle Anomalies in (3+1)d

TL;DR

This paper establishes an upper bound on 't Hooft anomalies in (3+1)d superconformal field theories using conformal bootstrap, linking anomalies to charged degrees of freedom and validating results with free fields and SQCD.

Contribution

It introduces a novel bound on flavor symmetry anomalies in (3+1)d SCFTs using bootstrap techniques, connecting anomalies to current two-point functions.

Findings

Bound on 't Hooft anomaly as a 3/2 power of current two-point coefficient

Validation of bounds with free fields and SQCD

Establishment of a quantitative relation between anomalies and degrees of freedom

Abstract

How many charged degrees of freedom are necessary to accommodate a certain amount of 't Hooft anomaly? Using the conformal bootstrap for the four-point function of flavor current multiplets, we show that in all (3+1)d superconformal field theories the 't Hooft anomaly of a continuous flavor symmetry is bounded from above by the 3/2 power of the current two-point function coefficient, which can be thought of as a measure for the amount of charged degrees of freedom. We check our bounds against free fields and SQCD in the conformal window.