Evidence for C-theorems in 6D SCFTs

TL;DR

This paper provides evidence for the existence of weak C-functions in 6D SCFTs, which decrease along RG flows, by analyzing anomaly polynomial coefficients and their behavior across various theories.

Contribution

It introduces a family of candidate C-functions in 6D SCFTs based on anomaly polynomial coefficients and maps their monotonic regions across different theories.

Findings

Identified regions in parameter space where C-functions decrease along flows

Confirmed the Euler density anomaly lies within the monotonic region

Mapped the shape of the unbounded monotonic region in m-space

Abstract

Using the recently established classification of 6D SCFTs we present evidence for the existence of families of weak C-functions, that is, quantities which decrease in a flow from the UV to the IR. Introducing a background R-symmetry field strength R and a non-trivial tangent bundle T on the 6D spacetime, we consider C-functions given by the linear combinations C = m1 alpha + m2 beta + m3 gamma, where alpha, beta and gamma are the anomaly polynomial coefficients for the formal characteristic classes c2(R)^2, c2(R)p1(T) and p1(T)^2. By performing a detailed sweep over many theories, we determine the shape of the unbounded monotonic region in "m-space" compatible with both Higgs branch flows and tensor branch flows. We also verify that --as expected-- the Euler density conformal anomaly falls in the admissible region.