EFT of 6D SUSY RG Flows

TL;DR

This paper develops the low energy effective field theory for 6D conformal and superconformal field theories, providing new insights into RG flows, symmetry breaking, and the 6D a-theorem, with implications for understanding tensionless strings.

Contribution

It derives the dilaton-axion effective action for 6D CFTs and SCFTs, offering a streamlined proof of the 6D a-theorem and exploring the possibility of interacting dilaton theories at strong coupling.

Findings

Proof of the 6D a-theorem for tensor branch flows

Constraints on Higgs and mixed branch flows in 6D SCFTs

Conjecture of interacting dilaton theories even with vanishing 4-derivative interactions

Abstract

Motivated by its potential use in constraining the structure of 6D renormalization group flows, we determine the low energy dilaton-axion effective field theory of conformal and global symmetry breaking in 6D conformal field theories (CFTs). While our analysis is largely independent of supersymmetry, we also investigate the case of 6D superconformal field theories (SCFTs), where we use the effective action to present a streamlined proof of the 6D a-theorem for tensor branch flows, as well as to constrain properties of Higgs branch and mixed branch flows. An analysis of Higgs branch flows in some examples leads us to conjecture that in 6D SCFTs, an interacting dilaton effective theory may be possible even when certain 4-dilaton 4-derivative interaction terms vanish, because of large momentum modifications to 4-point dilaton scattering amplitudes. This possibility is due to the fact that in all known $D > 4$ CFTs, the approach to a conformal fixed point involves effective strings which are becoming tensionless.