A String and M-theory Origin for the Salam-Sezgin Model

TL;DR

The authors establish a string/M-theory origin for the Salam-Sezgin six-dimensional chiral gauged supergravity by constructing a consistent Pauli-type reduction of type I (or heterotic) supergravity on a non-compact internal space ${\cal H}^{2,2}$ times $S^1$, embedding the Salam-Sezgin theory within a chain of reductions from 10D to 7D to 6D. Starting from the maximal $N=4$, $SO(5)$ gauged supergravity in $D=7$, they perform an Inönü–Wigner contraction to $SO(4)$ and then to a non-compact $SO(2,2)$ gauging, followed by a Kaluza reduction on $S^1$ to yield an $N=(1,1)$ six-dimensional theory, which is consistently truncated to the Salam-Sezgin $N=(1,0)$ model. The embedding is upliftable to ten dimensions, with a detailed ansatz that leads to a ten-dimensional Type I background; in the large-distance limit, the Salam-Sezgin Minkowski$_4\times S^2$ ground state approaches the NS5-brane near-horizon geometry, or, under S-duality, the D5-brane horizon in Type IIB. These results show that Salam-Sezgin can be obtained from non-compact higher-dimensional gaugings, and they provide a framework for uplifting its solutions to ten or eleven dimensions, linking lower-dimensional gauged supergravities to string/M-theory origins.

Abstract

An M/string-theory origin for the six-dimensional Salam-Sezgin chiral gauged supergravity is obtained, by embedding it as a consistent Pauli-type reduction of type I or heterotic supergravity on the non-compact hyperboloid ${\cal H}^{2,2}$ times $S^1$. We can also obtain embeddings of larger, non-chiral, gauged supergravities in six dimensions, whose consistent truncation yields the Salam-Sezgin theory. The lift of the Salam-Sezgin (Minkowski)$_4\times S^2$ ground state to ten dimensions is asymptotic at large distances to the near-horizon geometry of the NS5-brane.