Group Reduction of Heterotic Supergravity

TL;DR

This paper performs a detailed reduction of ten-dimensional heterotic supergravity on group manifolds, revealing new gauged supergravity models with duality symmetries and scalar couplings, and discusses their truncations and unique features.

Contribution

It introduces a new class of gauged supergravities from heterotic supergravity reductions, uncovering their duality symmetries and scalar structures, with explicit reduction formulas and truncation analyses.

Findings

Derived gauged supergravities with SO(n,n+dim K) duality symmetry.

Identified the gauge group as K×G⋉R^n and its implications.

Provided reduction formulas and analyzed truncation obstacles in d=6.

Abstract

The reduction of ten-dimensional heterotic supergravity with Yang-Mills symmetry group K is performed on an arbitrary n-dimensional group manifold G. The reduction involves a nonvanishing 3-form flux, and the Lie algebra of G must have traceless structure constants to ensure the consistency of the reduction at the level of the action. A large class of gauged supergravities in d=10-n with (non)compact gaugings is obtained. The resulting models describe half-maximal gauged supergravities coupled to $ (n + {\rm dim} K)$ vector multiplets. We uncover their hidden $SO(n,n+{\rm dim} K)$ duality symmetry, and the $SO(n,n+{\rm dim} K) / SO(n)\times SO(n+{\rm dim} K)$ coset structure that governs the couplings of the scalar fields. We find that the local gauge symmetry of the d-dimensional theory is $K\times G \ltimes R^n$. Differences from the existing gauged supergravities are highlighted. The consistent truncation to pure half-maximal gauged supergravity in any dimension is shown, and the obstacle to performing a chiral truncation of the theory in d=6 dimensions is found. Among the results obtained are the complete diagonalisation of the fermionic kinetic terms, and other reduction formulae that are applicable to group reductions of supergravities in arbitrary dimensions.