Fermions and D=11 Supergravity On Squashed Sasaki-Einstein Manifolds

TL;DR

This paper analyzes the reduction of fermionic modes in D=11 supergravity on squashed Sasaki-Einstein manifolds, deriving equations of motion and interactions relevant for holographic duals and superconductors.

Contribution

It provides the first detailed derivation of fermionic equations of motion and their couplings in this specific consistent truncation of supergravity.

Findings

Derived lower-dimensional fermionic equations of motion

Established couplings with charged scalars and form fields

Confirmed consistency with supersymmetric structure

Abstract

We discuss the dimensional reduction of fermionic modes in a recently found class of consistent truncations of D=11 supergravity compactified on squashed seven-dimensional Sasaki-Einstein manifolds. Such reductions are of interest, for example, in that they have $(2+1)$-dimensional holographic duals, and the fermionic content and their interactions with charged scalars are an important aspect of their applications. We derive the lower-dimensional equations of motion for the fermions and exhibit their couplings to the various bosonic modes present in the truncations under consideration, which most notably include charged scalar and form fields. We demonstrate that our results are consistent with the expected supersymmetric structure of the lower dimensional theory, and apply them to a specific example which is relevant to the study of $(2+1)$-dimensional holographic superconductors.