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Fermions and type IIB supergravity on squashed Sasaki-Einstein manifolds. (English) Zbl 1214.83040

Summary: 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 the \(U(1) \) 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.

MSC:

83E50 Supergravity
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
83E15 Kaluza-Klein and other higher-dimensional theories
81T60 Supersymmetric field theories in quantum mechanics
81R40 Symmetry breaking in quantum theory
82D55 Statistical mechanics of superconductors
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References:

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