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Type IIB supergravity on squashed Sasaki-Einstein manifolds

Davide Cassani, Gianguido Dall'Agata, Anton F. Faedo

TL;DR

This work constructs a consistent ${ m N}=4$ Kaluza–Klein truncation of type IIB supergravity on general squashed Sasaki–Einstein 5-manifolds, retaining the universal gauge-sector modes and a set of massive KK states. The resulting five-dimensional theory includes a gravity multiplet, two vector multiplets, and a tensor hierarchy whose couplings are fixed by an embedding tensor, yielding a gauge group $G={ m Heis}_3 imes{ m U}(1)_R$ and a scalar potential with two AdS vacua (one supersymmetric, one non-supersymmetric). The truncation is explicitly matched to ${ m N}=4$ gauged supergravity, with a detailed derivation of the ungauged and gauged sectors, covariant field strengths, and the role of RR flux $k$ in obstructing or enabling dualizations. The paper also analyzes the vacua and their spectra, discusses holographic RG flows between the AdS points, and outlines a web of possible further reductions to 4D and other ${ m N}=2$ or ${ m N}=4$ theories, thereby expanding the set of exact embeddings of 5D models into type IIB supergravity for AdS/CFT applications.

Abstract

We provide a consistent N=4 Kaluza-Klein truncation of type IIB supergravity on general 5-dimensional squashed Sasaki-Einstein manifolds. Our reduction ansatz keeps all and only the supergravity modes dual to the universal gauge sector of the associated conformal theories, via the gauge/gravity correspondence. The reduced 5-dimensional model displays remarkable features: it includes both zero-modes as well as massive iterations of the Kaluza-Klein operators on the internal manifold; it contains tensor fields dual to vectors charged under a non-abelian gauge group; it has a scalar potential with a non-supersymmetric AdS vacuum in addition to the supersymmetric one.

Type IIB supergravity on squashed Sasaki-Einstein manifolds

TL;DR

This work constructs a consistent Kaluza–Klein truncation of type IIB supergravity on general squashed Sasaki–Einstein 5-manifolds, retaining the universal gauge-sector modes and a set of massive KK states. The resulting five-dimensional theory includes a gravity multiplet, two vector multiplets, and a tensor hierarchy whose couplings are fixed by an embedding tensor, yielding a gauge group and a scalar potential with two AdS vacua (one supersymmetric, one non-supersymmetric). The truncation is explicitly matched to gauged supergravity, with a detailed derivation of the ungauged and gauged sectors, covariant field strengths, and the role of RR flux in obstructing or enabling dualizations. The paper also analyzes the vacua and their spectra, discusses holographic RG flows between the AdS points, and outlines a web of possible further reductions to 4D and other or theories, thereby expanding the set of exact embeddings of 5D models into type IIB supergravity for AdS/CFT applications.

Abstract

We provide a consistent N=4 Kaluza-Klein truncation of type IIB supergravity on general 5-dimensional squashed Sasaki-Einstein manifolds. Our reduction ansatz keeps all and only the supergravity modes dual to the universal gauge sector of the associated conformal theories, via the gauge/gravity correspondence. The reduced 5-dimensional model displays remarkable features: it includes both zero-modes as well as massive iterations of the Kaluza-Klein operators on the internal manifold; it contains tensor fields dual to vectors charged under a non-abelian gauge group; it has a scalar potential with a non-supersymmetric AdS vacuum in addition to the supersymmetric one.

Paper Structure

This paper contains 15 sections, 114 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Reducing IIB supergravity on squashed SE$_5$
  3. The reduction procedure
  4. The self-dual 5-form
  5. The 5-dimensional action
  6. Matching ${\cal N} = 4$ gauged supergravity
  7. The ungauged theory
  8. The gauged theory
  9. Discussion
  10. The supersymmetric vacuum
  11. The susy breaking vacuum
  12. Flows from and between the vacua
  13. Further reductions
  14. Conventions
  15. Reduction of the equations of motion

Figures (1)

  • Figure 1: Plot of the numerical solutions for the superpotential (light orange) and fake superpotential (dark blue). The dashed gray line represents $\sqrt{|{\cal V}_{\rm eff}|/6}$ as a function of $\sigma$.