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Equivariant localization and holography
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Equivariant localization and holography
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We discuss the theory of equivariant localization focussing on applications relevant for holography. We consider geometries comprising compact and non-compact toric orbifolds, as well as more general non-compact toric Calabi-Yau singularities. A key object in our constructions is the equivariant volume, for which we describe two methods of evaluation: the Berline-Vergne fixed-point formula and the Molien-Weyl formula, supplemented by the Jeffrey-Kirwan prescription. We present two applications in supersymmetric field theories. Firstly, we describe a method for integrating the anomaly polynomial of SCFTs on compact toric orbifolds. Secondly, we discuss equivariant orbifold indices that are expected to play a key role in the computation of supersymmetric partition functions. In the context of supergravity, we propose that the equivariant volume can be used to characterise universally the geometry of a large class of supersymmetric solutions. As an illustration, we employ equivariant localization to prove the factorization in gravitational blocks of various supergravity free energies, recovering previous results as well as obtaining generalizations.
Forward citations
Cited by 6 Pith papers
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Ten-dimensional localization
Equivariantly closed polyforms for type II Page fluxes and actions enable direct 10D localization of on-shell actions and flux quantization for minimally supersymmetric backgrounds.
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Finite-N indices for M5- and M2-branes are expressed via the same equivariant characteristic classes, generalizing M2/M5 duality through geometry exchange.
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Derives Airy representation for S^3 partition functions in M2-brane theories that exactly matches equivariant topological string predictions and proposes a new CY4 to C x CY3 correspondence via quantum curves.
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Equivariant localization for $D=5$ gauged supergravity
A method is given to compute the D=5 on-shell action via equivariant localization after dimensional reduction to D=4 N=2 gauged supergravity for solutions admitting both the R-symmetry Killing vector and an additional...
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Towards OSV in AdS
Derives Z_{S^1×S^2} ∼ |Z_{S^3_b}|^2 for 3d N=2 SCFTs and links it holographically to supersymmetric AdS4 black hole partition functions, akin to OSV.
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