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A supersymmetric consistent truncation for conifold solutions

Davide Cassani, Anton F. Faedo

TL;DR

This work constructs a supersymmetric, consistent truncation of type IIB supergravity on the T^{1,1} coset by including SU(2)×SU(2) invariant KK modes, yielding a 5D gauged N=4 supergravity with three vector multiplets. The truncation extends the Papadopoulos–Tseytlin ansatz to incorporate nontrivial cohomology (the Betti multiplet) and RR/NSNS fluxes, enabling a coherent holographic description of conifold dynamics, including new AdS_5 vacua and a rich spectrum of dual operators. It also exhibits several N=2 subtruncations compatible with Klebanov–Strassler physics and backreacting smeared D7-branes, and discusses the gauge/gravity dictionary for the SU(2)×SU(2) invariant sector. The results provide a robust five-dimensional framework for studying conifold backgrounds, their deformations, and associated holographic phenomena, with potential applications to holographic condensed matter and stringy corrections beyond the supergravity regime.

Abstract

We establish a supersymmetric consistent truncation of type IIB supergravity on the T^{1,1} coset space, based on extending the Papadopoulos-Tseytlin ansatz to the full set of SU(2)xSU(2) invariant Kaluza-Klein modes. The five-dimensional model is a gauged N=4 supergravity with three vector multiplets, which incorporates various conifold solutions and is suitable for the study of their dynamics. By analysing the scalar potential we find a family of new non-supersymmetric AdS_5 extrema interpolating between a solution obtained long ago by Romans and a solution employing an Einstein metric on T^{1,1} different from the standard one. Finally, we discuss some simple consistent subtruncations preserving N=2 supersymmetry. One of them still contains the Klebanov-Strassler solution, and is compatible with the inclusion of smeared D7-branes.

A supersymmetric consistent truncation for conifold solutions

TL;DR

This work constructs a supersymmetric, consistent truncation of type IIB supergravity on the T^{1,1} coset by including SU(2)×SU(2) invariant KK modes, yielding a 5D gauged N=4 supergravity with three vector multiplets. The truncation extends the Papadopoulos–Tseytlin ansatz to incorporate nontrivial cohomology (the Betti multiplet) and RR/NSNS fluxes, enabling a coherent holographic description of conifold dynamics, including new AdS_5 vacua and a rich spectrum of dual operators. It also exhibits several N=2 subtruncations compatible with Klebanov–Strassler physics and backreacting smeared D7-branes, and discusses the gauge/gravity dictionary for the SU(2)×SU(2) invariant sector. The results provide a robust five-dimensional framework for studying conifold backgrounds, their deformations, and associated holographic phenomena, with potential applications to holographic condensed matter and stringy corrections beyond the supergravity regime.

Abstract

We establish a supersymmetric consistent truncation of type IIB supergravity on the T^{1,1} coset space, based on extending the Papadopoulos-Tseytlin ansatz to the full set of SU(2)xSU(2) invariant Kaluza-Klein modes. The five-dimensional model is a gauged N=4 supergravity with three vector multiplets, which incorporates various conifold solutions and is suitable for the study of their dynamics. By analysing the scalar potential we find a family of new non-supersymmetric AdS_5 extrema interpolating between a solution obtained long ago by Romans and a solution employing an Einstein metric on T^{1,1} different from the standard one. Finally, we discuss some simple consistent subtruncations preserving N=2 supersymmetry. One of them still contains the Klebanov-Strassler solution, and is compatible with the inclusion of smeared D7-branes.

Paper Structure

This paper contains 20 sections, 99 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. The coset geometry
  3. Metric and curvature
  4. Left-invariant forms
  5. The dimensional reduction
  6. Reduction of the curvature
  7. Expansion of the form fields
  8. The five-dimensional model
  9. Compatibility with $\mathcal{N}=4$ supergravity
  10. Identification of the $\mathcal{N}=4$ fields via the ungauged theory
  11. The gauging and the embedding tensor
  12. A new family of AdS$_5$ solutions
  13. The dual operators
  14. $\mathcal{N}=2$ subtruncations and backreacting D7-branes
  15. Truncating to $\mathcal{N}=2$
  16. ...and 5 more sections

Figures (1)

  • Figure 1: Plot of the lowest mass$^2$ eigenvalue as a function of the $T^{1,1}$ metric parameter $t$. The horizontal line is the Breitenlohner--Freedman bound.