New Solution of D=11 Supergravity on S^7 from D=4

TL;DR

This paper presents new solutions in eleven-dimensional supergravity derived from four-dimensional gauged supergravity, including an interpolating solution and their pp-wave limits, with implications for AdS/CFT correspondence.

Contribution

It introduces a novel static partially twisted supergravity solution and its exact interpolating solution connecting different geometries, extending the understanding of D=11 supergravity on S^7.

Findings

Exact interpolating solution connecting AdS_4 and AdS_2×H_2 geometries.

Uplifted eleven-dimensional solutions including AdS_4×S^7 and AdS_2×H_2×S^7.

Penrose limits indicating supernumerary supersymmetry in the pp-wave regime.

Abstract

A new static partially twisted solution of N=4, SO(4) gauged supergravity in D=11 is obtained in this work using Cveti\^c et al embedding of four dimensional into eleven dimensional supergravities. In four dimensions we get two solutions: an asymptotic one corresponding to $AdS_4$ and a near horizon fixed point solution of the form $AdS_2\times H_2$. Hence, while the former solution has 32 supercharges the latter turns out to have only 4 conserved. Moreover, we managed to find an exact interpolating solution, thus connecting the above two. Aiming at a future study of $AdS/CFT$ duality for the theory at hand we derived the Penrose limit of the four dimensional solutions. Interestingly the pp-wave limit of the near horizon solution suggests itself as being of the supernumerary supersymmetric type. In D=11 we exhibit the uplift of the four dimensional solutions: one associated to $AdS_4\times S^7$ and the other to a foliation of $AdS_2\times H_2 \times S^7$, as well as their pp-wave limits.