Consistent Warped $\mathbb{R}\times T^{1,1}$ Reduction of Heterotic Supergravity

Abstract

We find a curious duality between the bosonic sector of heterotic supergravity and the noncritical bosonic string with conformal anomaly. This allows us to map the Mink${}_4\times S^3\times S^3$ vacuum of the bosonic string to a new warped $\mathbb{R}\times (T^{1,1}\times$Mink${}_4)$ vacuum of the heterotic theory, which turns out to be supersymmetric, preserving $1/4$ of the supersymmetry. We perform consistent dimensional reduction of the heterotic theory on the warped $\mathbb{R}\times T^{1,1}$ internal space and obtain $\mathcal{N}=1$, $D=4$ supergravity, with one complex scalar multiplet and $SU(2)\times SU(2)$ Yang-Mills multiplets, where the gauge symmetry is originated from the isometry group of $T^{1,1}$.

27 pages, fixed typos, references added, to appear in JHEP