Fermions and Type IIB Supergravity On Squashed Sasaki-Einstein Manifolds

TL;DR

This paper studies fermionic modes in type IIB supergravity on squashed Sasaki-Einstein manifolds, deriving effective equations, analyzing supersymmetry, and exploring applications to holographic superconductors with charged massive modes.

Contribution

It provides a consistent truncation including massive charged fermions and analyzes their role in holographic superconductor models.

Findings

Derived lower-dimensional fermionic equations of motion.

Identified fermion masses around two AdS5 vacua with different supersymmetry.

Constructed a truncated fermion sector with a single spin-1/2 mode.

Abstract

We discuss the dimensional reduction of fermionic modes in a recently found class of consistent truncations of type IIB supergravity compactified on squashed five-dimensional Sasaki-Einstein manifolds. We derive the lower dimensional equations of motion and effective action, and comment on the supersymmetry of the resulting theory, which is consistent with N=4 gauged supergravity in $d=5$, coupled to two vector multiplets. We compute fermion masses by linearizing around two $AdS_{5}$ vacua of the theory: one that breaks N=4 down to N=2 spontaneously, and a second one which preserves no supersymmetries. The truncations under consideration are noteworthy in that they retain massive modes which are charged under a U(1) subgroup of the $R$-symmetry, a feature that makes them interesting for applications to condensed matter phenomena via gauge/gravity duality. In this light, as an application of our general results we exhibit the coupling of the fermions to the type IIB holographic superconductor, and find a consistent further truncation of the fermion sector that retains a single spin-1/2 mode.