A bound on 6D N=1 supergravities

TL;DR

This paper proves that in 6D chiral (1,0) supergravity with one tensor multiplet, only finitely many gauge groups and matter representations are possible, based on anomaly cancellation and positivity of kinetic terms.

Contribution

It establishes a finiteness result for gauge groups and matter content in 6D chiral supergravity theories using low-energy consistency conditions.

Findings

Finite set of gauge groups and matter representations identified.

Constraints derived solely from anomaly cancellation and positivity conditions.

Result does not extend to non-chiral (1,1) supergravities.

Abstract

We prove that there are only finitely many distinct semi-simple gauge groups and matter representations possible in consistent 6D chiral (1,0) supergravity theories with one tensor multiplet. The proof relies only on features of the low-energy theory; the consistency conditions we impose are that anomalies should be cancelled by the Green-Schwarz mechanism, and that the kinetic terms for all fields should be positive in some region of moduli space. This result does not apply to the case of the non-chiral (1,1) supergravities, which are not constrained by anomaly cancellation.