D=5 SU(2)xU(1) Gauged Supergravity from D=11 Supergravity

TL;DR

This paper constructs a comprehensive reduction ansatz from eleven-dimensional supergravity to five-dimensional SU(2)×U(1) gauged supergravity for a broad class of supersymmetric solutions, enabling uplift of solutions and analysis of dual N=2 superconformal field theories.

Contribution

It provides the full non-linear Kaluza-Klein reduction ansatz for D=11 supergravity on general internal manifolds N_6, facilitating solution uplift and dual field theory analysis.

Findings

Constructed the general non-linear reduction ansatz for arbitrary N_6.

Enabled uplift of five-dimensional solutions to eleven dimensions.

Applied the framework to a specific N_6 related to M5-branes wrapping holomorphic curves.

Abstract

We consider the most general class of supersymmetric solutions of D=11 supergravity consisting of a warped product of AdS_5 with a six-dimensional internal manifold N_6, which are dual to N=2 super conformal field theories in d=4. For any such N_6 we construct the full non-linear Kaluza-Klein ansatz for the reduction of D=11 supergravity on N_6 down to D=5 SU(2)xU(1) gauged supergravity, at the level of the bosonic fields. This allows one to uplift any solution of the D=5 supergravity to obtain a solution of D=11 supergravity for any given N_6. Using an explicit N_6, corresponding to M5-branes wrapping holomorphic curves in a Calabi-Yau two-fold, we uplift some solutions and comment upon their interpretation.