On The Consistent Supersymmetric Reduction Of Heterotic Supergravity With Geometrically Arising Yang-Mills Symmetries

TL;DR

This paper extends a heterotic supergravity compactification on a warped product space to include fermionic fields, resulting in a consistent reduction to ungauged =1 supergravity with Yang-Mills and scalar multiplets.

Contribution

It demonstrates that the previously known bosonic consistent truncation can be extended to include fermionic sectors, ensuring a fully consistent reduction.

Findings

Achieved a consistent fermionic truncation in heterotic supergravity.

Reduced the theory to ungauged =1 supergravity with Yang-Mills and scalar multiplets.

Confirmed the preservation of supersymmetry in the reduced model.

Abstract

In the paper arXiv:2501.04771, a novel compactification of heterotic supergravity on a warped product of $\R\times T^{1,1}$ was constructed, where $T^{1,1}$ is a five-dimensional coset space $(SU(2)\times SU(2))/U(1)$. It was shown that this admits a four dimensional Minkowski vacuum solution with ${\cal N}=1$ supersymmetry, and furthermore that in the bosonic sector there exists a remarkable fully consistent truncation in which the gauge bosons of the $SU(2)\times SU(2)$ isometries of the $T^{1,1}$ are retained. In this paper, we examine this reduction further, and show that the consistency can be extended to include the fermionic sector also. Thus the heterotic theory admits a consistent reduction to give an ungauged ${\cal N}=1$ supergravity coupled to $SU(2)\times SU(2)$ Yang-Mills multiplets and a scalar multiplet.