A consistent truncation of IIB supergravity on manifolds admitting a Sasaki-Einstein structure

TL;DR

The paper constructs a five-dimensional, non-supersymmetric consistent truncation of type IIB supergravity on Sasaki-Einstein manifolds, retaining gravity and five real scalar fields. It further exhibits a three-scalar truncation and a one-parameter single-scalar family, each supporting supersymmetric and non-supersymmetric AdS vacua, including $AdS_5$ and $AdS_4\times\mathbb{R}$ solutions, with explicit uplift to ten dimensions. A fluctuation analysis around the AdS critical points identifies a dilaton flat direction in the SUSY case and maps the spectra to dual operators ${\cal O}_3$, ${\cal O}_4$, ${\cal O}_6$, ${\cal O}_7$, ${\cal O}_8$ (and an extra dimension $2(1+\sqrt{3})$ in the non-SUSY case), demonstrating a closed OPE structure within the truncation. The results provide a robust framework for holography of Sasaki-Einstein compactifications and offer clear avenues for constructing a holographic dictionary and exploring related solutions, including potential Janus configurations.

Abstract

We present a consistent truncation of IIB supergravity on manifolds admitting a Sasaki-Einstein structure, which keeps the metric and five real scalar fields. This theory can be further truncated to a constrained one-parameter family that depends on only the metric and one scalar, as well as to a theory with a metric and three scalars. The reduced theory admits supersymmetric and non-supersymmetric AdS_5 and AdS_4 x R solutions. We analyze the spectrum around the AdS critical points and identify the dual operators.