Uniqueness of D=8 minimal supergravity with two vector multiplets

TL;DR

This paper investigates the unique consistent theory of minimal supergravity with two vector multiplets in eight dimensions, constrained by duality symmetries, anomaly cancellation, and gauge enhancement conditions.

Contribution

It demonstrates that these constraints uniquely determine the theory's couplings, especially in the BPS sector, and rules out gravitational contributions to the Bianchi identity.

Findings

Identifies a unique consistent theory under duality symmetry assumptions.

Shows that gravitational contributions to the Bianchi identity are not allowed.

Constrains couplings using anomaly cancellation and gauge enhancement loci.

Abstract

There exist only four known string theories with minimal supersymmetry in eight dimensions, whose low energy effective descriptions are given by minimal supergravity coupled to $l=18$, $10$, or $2$ vector multiplets. It has been argued that these numbers are uniquely fixed by consistency conditions of the effective theory. In this work, we investigate the protected couplings of minimal supergravity coupled to two vector multiplets under the assumption that the theory admits a duality symmetry of the form $\Gamma_0(N)\times \Gamma_0(N)\subset {\rm SL}(2,\mathbb{Z}) \times {\rm SL}(2,\mathbb{Z})$ for some positive integer $N$. We show that consistency with anomaly cancellation, higher-dimensional uplifts, and gauge enhancement loci strongly constrains the allowed couplings and isolates a unique consistent theory in the BPS sector. In particular, we find that the Bianchi identity for the three-form flux cannot have gravitational contributions.