Conformal a-anomaly of some non-unitary 6d superconformal theories

TL;DR

This paper calculates the conformal anomaly a-coefficient for certain non-unitary 6d superconformal theories, revealing new anomaly cancellation results and connections to higher-dimensional supergravity and string theory.

Contribution

It introduces a method linking 6d and 7d determinants to compute anomalies and demonstrates anomaly cancellation in specific 6d supergravity models.

Findings

The (1,0) supermultiplet with a 4-derivative gauge-invariant vector has the same a-anomaly as the standard vector multiplet.

Higher derivative (2,0) 6d conformal supergravity coupled to 26 tensor multiplets has zero a-anomaly.

Certain ghost-like tensor multiplet configurations lead to anomaly-free IR theories related to string compactifications.

Abstract

We compute the conformal anomaly a-coefficient for some non-unitary (higher derivative or non-gauge-invariant) 6d conformal fields and their supermultiplets. We use the method based on a connection between 6d determinants on S^6 and 7d determinants on AdS_7. We find, in particular, that (1,0) supermultiplet containing 4-derivative gauge-invariant conformal vector has precisely the value of a-anomaly as attributed in arXiv:1506.03807 (on the basis of R-symmetry and gravitational 't Hooft matching) to the standard (1,0) vector multiplet. We also show that higher derivative (2,0) 6d conformal supergravity coupled to exactly 26 (2,0) tensor multiplets has vanishing a-anomaly. This is the 6d counterpart of the known fact of cancellation of the conformal anomaly in the 4d system of N=4 conformal supergravity coupled to 4 vector N=4 multiplets. In the case when 5 of tensor multiplets are chosen to be ghost-like and the conformal symmetry is spontaneously broken by a quadratic scalar constraint the resulting IR theory may be identified with (2,0) Poincare supergravity coupled to 21=26-5 tensor multiplets. The latter theory is known to be special: it is gravitational anomaly free and results upon compactification of 10d type IIB supergravity on K3.