Dimensional reduction of higher derivative heterotic supergravity

TL;DR

This paper derives higher derivative couplings of hypermultiplets in 6D supergravity from 10D heterotic supergravity, revealing the emergence of an $SO(4,4)$ symmetry through dimensional reduction and field redefinitions.

Contribution

It demonstrates the dimensional reduction process including higher derivative corrections and clarifies the emergence of $SO(4,4)$ symmetry at the field theory level.

Findings

Hypermultiplet scalars parametrize $SO(4,4)/(SO(4)\times SO(4))$

Field redefinitions restore $SO(4)$ symmetry in the action

Simplification achieved using torsionful spin connection in Chern-Simons term

Abstract

Higher derivative couplings of hypermultiplets to $6D, N=(1,0)$ supergravity are obtained from dimensional reduction of 10D heterotic supergravity that includes order $\alpha'$ higher derivative corrections. Reduction on $T^4$ is followed by a consistent truncation. In the resulting action the hyperscalar fields parametrize the coset $SO(4,4)/(SO(4)\times SO(4))$. While the $SO(4,4)$ symmetry is ensured by Sen's construction based on string field theory, its emergence at the field theory level is a nontrivial phenomenon. A number of field redefinitions in the hypermultiplet sector are required to remove several terms that break the $SO(4)\times SO(4)$ down to its $SO(4)$ diagonal subgroup in the action and the supersymmetry transformation rules. Working with the Lorentz Chern-Simons term modified 3-form field strength, where the spin connection has the 3-form field strength as torsion, is shown to simplify considerably the dimensional reduction.