Conformal anomaly c-coefficients of superconformal 6d theories

TL;DR

The paper derives linear relations that express the 6d $(1,0)$ conformal c-coefficients in terms of the chiral anomaly data $(\alpha,\beta,\gamma,\delta)$, with extra constraints $q_1=0$ for $(1,0)$ and $q_2=0$ for $(2,0)$ supersymmetry. It validates these relations across free multiplets, families of higher-derivative $(1,0)$ and $(2,0)$ multiplets, and select interacting theories (such as E-string and orbifold M5 models), and it connects to holographic results via 7d gravitational actions including $R^2$ and $R^3$ corrections. The work also demonstrates holographic subleading corrections and provides explicit anomaly data for higher-dimensional supergravity multiplets, including anomaly cancellation in the $(2,0)$ case when coupled to 26 tensor multiplets. Collectively, these results bolster a unified, supersymmetry-consistent framework for 6d conformal anomalies and their holographic realizations.

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.