The on-shell action of odd-dimensional supergravity with Chern-Simons terms localizes to fixed points via relative equivariant cohomology, yielding a universal formula matching M5-brane and black ring physics.
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Equivariant Localization in Supergravity
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abstract
We show that supersymmetric supergravity solutions with an R-symmetry Killing vector are equipped with a set of equivariantly closed forms. Various physical observables may be expressed as integrals of these forms, and then evaluated using the Berline-Vergne-Atiyah-Bott fixed point theorem. We illustrate with a variety of holographic examples, including on-shell actions, black hole entropies, central charges, and scaling dimensions of operators. The resulting expressions depend only on topological data and the R-symmetry vector, and hence may be evaluated without solving the supergravity equations.
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hep-th 8representative citing papers
Equivariant localization computes probe D3-brane actions in uplifted Kerr-Newman-AdS5 supergravity backgrounds, reducing them to toric-data integrals for SCFT indices.
New AdS3 x Y7 solutions in type IIB supergravity with spindle bases and hyperscalars dual to 2d N=(0,2) SCFTs, featuring non-coprime spindle integers and vanishing hyperscalars at poles for non-vanishing U(1)B flux.
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 Killing vector.
Equivariant localization computes the on-shell action of supersymmetric D=5 AdS rotating charged black holes in higher-derivative supergravity, matching the dual superconformal index in a Cardy-like limit.
Equivariantly closed forms in D=4 N=2 conformal supergravity allow closed-form supersymmetric observables in higher derivative theories without solving equations of motion.
New classes of supersymmetric AdS₂×Σ spindle solutions with hyperscalars are constructed in D=4 STU gauged supergravity and uplifted to smooth AdS₂×Y₉ solutions in D=11 supergravity.
citing papers explorer
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Odd-Dimensional Localization in Supergravity
The on-shell action of odd-dimensional supergravity with Chern-Simons terms localizes to fixed points via relative equivariant cohomology, yielding a universal formula matching M5-brane and black ring physics.
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Probing black holes with equivariant localization
Equivariant localization computes probe D3-brane actions in uplifted Kerr-Newman-AdS5 supergravity backgrounds, reducing them to toric-data integrals for SCFT indices.
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Spindle solutions, hyperscalars and smooth uplifts
New AdS3 x Y7 solutions in type IIB supergravity with spindle bases and hyperscalars dual to 2d N=(0,2) SCFTs, featuring non-coprime spindle integers and vanishing hyperscalars at poles for non-vanishing U(1)B flux.
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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 Killing vector.
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The superconformal index and localizing higher derivative supergravity
Equivariant localization computes the on-shell action of supersymmetric D=5 AdS rotating charged black holes in higher-derivative supergravity, matching the dual superconformal index in a Cardy-like limit.
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Equivariant localization for higher derivative supergravity
Equivariantly closed forms in D=4 N=2 conformal supergravity allow closed-form supersymmetric observables in higher derivative theories without solving equations of motion.
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Spindle solutions with hyperscalars in $D=4$ gauged supergravity
New classes of supersymmetric AdS₂×Σ spindle solutions with hyperscalars are constructed in D=4 STU gauged supergravity and uplifted to smooth AdS₂×Y₉ solutions in D=11 supergravity.
- Indices of M5 and M2 branes at finite $N$ from equivariant volumes, and a new duality