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

TL;DR

This work completes the program of a consistent dimensional reduction of ten-dimensional heterotic supergravity on the internal space $\mathbb{R}\times T^{1,1}$ by constructing the full fermionic reduction in addition to the previously established bosonic truncation. The resulting four-dimensional theory is ungauged ${\cal N}=1$ supergravity coupled to a scalar multiplet and an $SU(2)\times SU(2)$ Yang-Mills multiplet, with the non-Abelian gauge symmetry arising geometically from the $T^{1,1}$ isometries. The analysis connects to a dual DeWitt/groupp-manifold viewpoint and discusses pseudo-supersymmetry in the dual bosonic string context, highlighting the broader significance for coset reductions and the geometric emergence of gauge symmetries. The results provide a concrete, fully consistent supersymmetric truncation with potential implications for string compactifications and holography in heterotic frameworks.

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.