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

TL;DR

The paper extends the computation of conformal a‑anomalies to non‑unitary 6d conformal fields using an AdS7 determinant framework, yielding a universal a(Delta; h) formula and associated Casimir energy. It provides explicit a and E_c values for low‑spin unitary and non‑unitary multiplets, and shows that certain higher‑derivative vector multiplets reproduce anomaly values previously attributed to standard unitary multiplets. A striking result is that (2,0) conformal supergravity coupled to exactly 26 tensor multiplets has vanishing a‑anomaly and Casimir energy, pointing to an anomaly‑free, UV‑finite scenario and offering a 6d analogue of known 4d cancellations; the discussion also covers IR broken phases yielding a 21 tensor multiplet theory tied to Type IIB on K3 and potential links to 2d chiral algebras. Together, these findings illuminate the structure of conformal anomalies in 6d and their delicate interplay with supersymmetry, higher derivatives, and holographic methods, with implications for UV completions and 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.