Conformal anomaly c-coefficients of superconformal 6d theories

TL;DR

This paper establishes relations between conformal and chiral anomalies in 6d superconformal theories, verifying them through examples and exploring implications for various multiplets and holographic corrections.

Contribution

It introduces new formulas linking conformal anomaly coefficients to chiral anomalies in 6d theories, extending previous results and analyzing specific multiplets and holographic effects.

Findings

Validated anomaly relations on multiple multiplets

Proved anomaly cancellation in (2,0) 6d supergravity with 26 tensor multiplets

Predicted c-coefficients for E-string and orbifold M5-brane theories

Abstract

We propose general relations between the conformal anomaly and the chiral (R-symmetry and gravitational) anomaly coefficients in 6d (1,0) superconformal theories. The suggested expressions for the three type B conformal anomaly c-coefficients complement the expression for the type A anomaly a-coefficient found in arXiv:1506.03807. We check them on several examples -- the standard (1,0) hyper and tensor multiplets as well as some higher derivative short multiplets containing vector fields that generalize the superconformal 6d vector multiplet discussed in arXiv:1506.08727. We also consider a family of higher derivative superconformal (2,0) 6d multiplets associated to 7d multiplets in the KK spectrum of 11d supergravity compactified on S^4. In particular, we prove that (2,0) 6d conformal supergravity coupled to 26 tensor multiplets is free of all chiral and conformal anomalies. We discuss some interacting (1,0) superconformal theories, predicting the c-coefficients for the "E-string" theory on multiple M5-branes at E_8 9-brane and for the theory describing M5-branes at an orbifold singularity. Finally, we elaborate on holographic computation of subleading corrections to conformal anomaly coefficients coming from R^2+R^3 terms in 7d effective action, revisiting, in particular, the (2,0) theory case.