BPS states in type IIB SUGRA with $SO(4)\times SO(2)_{gauged} symmetry

TL;DR

This work extends the 1/2-BPS, $SO(4)\times SO(2)$-symmetric sector of type IIB supergravity by gauging the $SO(2)$ with a $U(1)$ field, allowing a more general Killing spinor charge $n$. Through a symmetry-guided reduction on $S^{3}\times S^{1}$, a four-dimensional Kahler base is identified, and the remaining data are governed by a Monge–Ampère–type equation and a nonlinear constraint, with the gauge field encoded by a scalar $\Phi$ and subject to Bianchi-consistency conditions implying $\mathcal{F}\wedge\mathcal{F}=2(n+2\alpha)(n+\alpha)\, y^{-4}\,\mathcal{J}\wedge\mathcal{J}$. The construction reproduces known ungauged, LLM, and AdS$_5\times$Sasaki–Einstein geometries as special cases, thereby unifying these solutions within a gauged framework. The results clarify how the $U(1)$ charge $n$ tunes between solution classes and highlight the persistence of a Kahler base with a scalar degree of freedom related to the Kahler potential. The paper also points toward nontrivial avenues for a matrix-model interpretation and giant-graviton backreaction in this less supersymmetric setting.

Abstract

We present an extension of our construction (hep-th/0606199) exhibiting $SO(4)\times SO(2)$ symmetry. We extend the previously presented ansatz by introducing a U(1) gauge field. The presence of the gauge field allows for more general values of the Killing spinor U(1) charge. One more time we identify a four dimensional Kahler structure and a Monge-Ampere type of equation parametrized by the U(1) Killing spinor charge. In addition we identify 2 scalars that parametrize the supersymmetric solutions, one of which is the Kahler potential.