Holography and equivariant localization in supergravity
File(s)
Author(s)
Jiao, Yusheng
Type
Thesis or dissertation
Abstract
In this thesis, we develop several frameworks for applying equivariant localization in 4D N=2gauged supergravity and explore its implications for holography. We will also discuss several possible extensions to 5D N=2 gauged supergravity. The central idea is that supersymmetric solutions naturally admit a Killing vector and associated equivariant structures. Applying equivariant localization allows us to calculate observables without detailed knowledge of the full solution, as contributions from the fixed points of the Killing vector.
We begin by studying near-horizon geometries AdS2M2 arising from 4D supersymmetric magnetically charged black holes in N=2 gauged supergravity. By reducing on AdS2, we perform localization on M2 to obtain the off-shell entropy function. We also extend the analysis to AdS3*M2 solutions in 5D N=2 gauged supergravity.
We then generalize this application to arbitrary supersymmetric asymptotically Euclidean AdS4 solutions in 4D N=2 gauged supergravity to calculate the gravitational free energy. Localization provides a universal fixed-point formula applicable to a broad class of supersymmetric solutions. We apply this to the STU model, where it reproduces known results and yields predictions for unknown solutions in both gravity and field theory.
Next, we extend the framework to the STU model coupled with a truncated hypermultiplet. The theory admits two AdS4 vacua holographically dual to the ABJM and mABJM theories. We demonstrate that the localization results from the STU model remain largely unchanged, while the hyperscalar introduces additional constraints on the fixed-point data. The resulting free energy functions reproduce the large-N free energies of both ABJM and mABJM theory.
Finally, we consider a special class of 4D supergravity obtained by dimensional reduction of 5D N=2 gauged supergravity on a circle. Applying the 4D results allows us to compute the gravitational free energies associated with AdS5 backgrounds and supersymmetric black holes, reproducing known results after appropriate boundary renormalization.
We begin by studying near-horizon geometries AdS2M2 arising from 4D supersymmetric magnetically charged black holes in N=2 gauged supergravity. By reducing on AdS2, we perform localization on M2 to obtain the off-shell entropy function. We also extend the analysis to AdS3*M2 solutions in 5D N=2 gauged supergravity.
We then generalize this application to arbitrary supersymmetric asymptotically Euclidean AdS4 solutions in 4D N=2 gauged supergravity to calculate the gravitational free energy. Localization provides a universal fixed-point formula applicable to a broad class of supersymmetric solutions. We apply this to the STU model, where it reproduces known results and yields predictions for unknown solutions in both gravity and field theory.
Next, we extend the framework to the STU model coupled with a truncated hypermultiplet. The theory admits two AdS4 vacua holographically dual to the ABJM and mABJM theories. We demonstrate that the localization results from the STU model remain largely unchanged, while the hyperscalar introduces additional constraints on the fixed-point data. The resulting free energy functions reproduce the large-N free energies of both ABJM and mABJM theory.
Finally, we consider a special class of 4D supergravity obtained by dimensional reduction of 5D N=2 gauged supergravity on a circle. Applying the 4D results allows us to compute the gravitational free energies associated with AdS5 backgrounds and supersymmetric black holes, reproducing known results after appropriate boundary renormalization.
Version
Open Access
Date Issued
2026-06-08
Date Awarded
2026-09-01
Copyright Statement
Attribution-NonCommercial 4.0 International Licence (CC BY-NC)
License URL
Advisor
Gauntlett, Jerome
Publisher Department
Department of Physics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)