arXiv subjects

Jerome P. Gauntlett

Publications and source records attributed to Jerome P. Gauntlett.

At least 19 recordsLinked to original sources

arXiv2026

Airy functions from quantum M-theory

We show that Airy function partition functions for M2-brane theories may be derived from relative equivariant localization of quantum M-theory. The eleven-dimensional Chern--Simons coupling gives the cubic term in the grand potential, while the $X_8$ correction gives the charge shift. Fixing the M2-brane charge turns the localized M-theory path integral into an Airy integral. In this way we derive the ABJM result, its toric Calabi--Yau generalizations, and gravitational blocks for black holes and other spacetimes, up to the prefactor and non-perturbative corrections.

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arXiv2026

Odd-Dimensional Localization in Supergravity

We establish a localization principle for odd-dimensional supergravity theories containing Chern--Simons interactions. Our construction relies on combining an equivariant extension of the gauge-invariant part of the action with an equivariant completion of the Chern--Simons anomaly form $Φ^{(\text{anom})}$ to form a relative equivariant cohomology class. This leads to a universal fixed point formula for the on-shell action of supersymmetric solutions that is expressed in terms of $Φ^{(\text{anom})}$ and an equivariant Euler class. We illustrate the formalism in $D=11$ and $D=5$ supergravity, with applications including the supersymmetric Casimir energy and superconformal index of M5-branes, as well as black ring and black lens solutions.

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arXiv2026

The superconformal index and localizing higher derivative supergravity

We show how equivariant localization can be used to compute the on-shell action for supersymmetric $D=5$ $AdS$ rotating, charged black holes in theories of supergravity with higher derivatives. An exact match with a dual field theory computation of the superconformal index in a Cardy-like limit is achieved.

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arXiv2026

Spindle solutions, hyperscalars and smooth uplifts

We construct $AdS_3\times Y_7$ solutions of type IIB supergravity, where $Y_7$ is a smooth $S^5$ bundle over a spindle $Σ(n_N,n_S)$, which are dual to $\mathcal{N}=(0,2)$ SCFTs in $d=2$. The solutions are constructed using the $D=5$ STU $U(1)^3$ gauged supergravity theory coupled to a hyperscalar charged under $U(1)_B$. We investigate spindle solutions with two new features: first, we allow $(n_N,n_S)$ to be non-coprime integers, including orbifolds of the round $S^2$, which can lead to non-unique, inequivalent uplifts, distinguished by the hyperscalar spectra, for given magnetic flux through the spindle. Second, we also allow the hyperscalar to vanish at the poles leading to solutions carrying non-vanishing $U(1)_B$ flux. The new hyperscalar $AdS_3$ solutions can naturally arise as the endpoint of RG flows, triggered by relevant hyperscalar deformations of the $AdS_3$ solutions of the STU model.

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arXiv2026

Equivariant localization for $D=5$ gauged supergravity

We consider supersymmetric solutions of $D=5$ Euclidean gauged supergravity coupled to an arbitrary number of vector multiplets. We consider solutions that admit both the R-symmetry Killing vector, $\mathcal{K}$, constructed as a bilinear in the Killing spinor, as well as an additional Killing vector $\ell$. Using $\ell$ to perform a dimensional reduction to $D=4$, $\mathcal{N}=2$ gauged supergravity, we show how the $D=5$ on-shell action can be computed using equivariant localization. We illustrate the formalism with some examples, computing the supersymmetric Casimir energy and the supersymmetric index of the dual SCFT without using the explicit supergravity solutions.

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arXiv2026

Spindle solutions with hyperscalars in $D=4$ gauged supergravity

We construct new classes of supersymmetric $AdS_2\times Σ$ solutions, where $Σ=Σ(n_N,n_S)$ is a spindle. Such solutions can arise as the near horizon limit of supersymmetric, accelerating black holes. The solutions are constructed using $D=4$ STU $U(1)^4$ gauged supergravity theory coupled to a charged hyperscalar, and can be uplifted to obtain smooth, supersymmetric $AdS_2\times Y_9$ solutions of $D=11$ supergravity. We allow $(n_N,n_S)$ to be non-coprime integers, including orbifolds of the round $S^2$. We also allow the hyperscalar to vanish at the poles. The $AdS_2$ solutions with non-vanishing hyperscalar can naturally arise as the endpoint of holographic RG flows, triggered by relevant hyperscalar deformations of the $AdS_2$ solutions of the STU model.

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arXiv2026

Equivariant localization for higher derivative supergravity

Conformal supergravity provides an effective off-shell formalism to study higher derivative actions. We show that the $D=4$, $\mathcal{N}=2$ theory admits equivariantly closed forms. These may be used to compute closed-form expressions for supersymmetric observables in a general class of supergravity theories with higher derivative couplings, without any need to solve equations of motion. We discuss applications to holography, presenting results for on-shell actions that are conjecturally valid to all orders in the perturbative $1/N$ expansion.

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arXiv2025

Equivariant localization for $D=4$ gauged supergravity

We consider supersymmetric solutions of $D=4$, $\mathcal{N}=2$ Euclidean gauged supergravity coupled to an arbitrary number of vector multiplets. Such solutions admit an R-symmetry Killing vector, $ξ$, constructed as a bilinear in the Killing spinor. The Killing spinor bilinears can also be used to construct polyforms that are equivariantly closed under the action of the equivariant exterior derivative $\mathrm{d}_ξ=\mathrm{d}-ξ\mathbin{\rule[.2ex]{.4em}{.03em}\rule[.2ex]{.03em}{.9ex}}\,$. This allows one to compute various flux integrals and the on-shell action using localization, without solving any supergravity equations, just assuming the supersymmetric solutions exist. The flux integrals allow one to obtain important UV-IR relations, relating fixed point data in the bulk to data on the asymptotic AdS boundary, allowing one to express the gravitational free energy in terms of boundary SCFT data. We illustrate the formalism with a number of examples, including classes of solutions which are unlikely to ever be constructed in closed form.

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arXiv2025

Sasaki-Einstein Geometry, GK Geometry and the AdS/CFT correspondence

We review various aspects of Sasaki-Einstein and GK geometry, emphasising their similarities, interconnections and significance for the AdS/CFT correspondence. In particular, we highlight the key role that physical considerations have played in formulating geometric extremization principles, which have been instrumental in both understanding the geometry and identifying the corresponding dual field theories.

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arXiv2025

Toric gravitational instantons in gauged supergravity

We introduce a general class of toric gravitational instantons in $D=4$, $\mathcal{N}=2$ gauged supergravity, namely Euclidean supersymmetric solutions with $U(1)^2$ isometry. Such solutions are specified by a "supergravity labelled polytope", where the labels encode the 4-manifold topology, the choice of magnetic fluxes, and certain signs associated to the Killing spinor. Equivariant localization then allows us to write down the gravitational free energy for such a solution, assuming it exists, and study its properties. These results open the way for a systematic study of holography in this setting, where the dual large $N$ field theories are defined on the boundary 3-manifolds, which are (squashed) lens spaces $L(p,q)$ or generalizations with orbifold singularities.

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arXiv2025

Localization of the free energy in supergravity

We derive a general formula for the gravitational free energy of Euclidean supersymmetric solutions to $D=4$, $\mathcal{N}=2$ gauged supergravity coupled to vector multiplet matter. This allows one to compute the free energy without solving any supergravity equations, just assuming the solutions exist. As well as recovering some known results in the literature with ease, we also present new supergravity results that match with holographically dual field theory computations.

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arXiv2024

Superconformal Monodromy Defects in ABJM and mABJM Theory

We study $D=11$ supergravity solutions which are dual to one-dimensional superconformal defects in $d=3$ SCFTs. We consider defects in ABJM theory with monodromy for $U(1)^4\subset SO(8)$ global symmetry, as well as in $\mathcal{N}=2$ mABJM SCFT, which arises from the RG flow of a mass deformation of ABJM theory, with monodromy for $U(1)^3\subset SU(3)\times U(1)$ global symmetry. We show that the defects of the two SCFTs are connected by a line of bulk marginal mass deformations and argue that they are also related by bulk RG flow. In all cases we allow for the possibility of conical singularities at the location of the defect. Various physical observables of the defects are computed including the defects conformal weight and the partition function, as well as associated supersymmetric Renyi entropies.

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arXiv2024

Superconformal Monodromy Defects in $\mathcal{N}$=4 SYM and LS theory

We study type IIB supergravity solutions that are dual to two-dimensional superconformal defects in $d=4$ SCFTs which preserve $\mathcal{N}=(0,2)$ supersymmetry. We consider solutions dual to defects in $\mathcal{N}=4$ SYM theory that have non-trivial monodromy for $U(1)^3\subset SO(6)$ global symmetry and we also allow for the possibility of conical singularities. In addition, we consider the addition of fermionic and bosonic mass terms that have non trivial dependence on the spatial directions transverse to the defect, while preserving the superconformal symmetry of the defect. We compute various physical quantities including the central charges of the defect expressed as a function of the monodromy, the on-shell action as well as associated supersymmetric Renyi entropies. Analogous computations are carried out for superconformal defects in the $\mathcal{N}=1$, $d=4$ Leigh-Strassler SCFT. We also show that the defects of the two SCFTs are connected by a line of bulk marginal mass deformations and argue that they are also related by bulk RG flow.

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arXiv2024

Localization and Attraction

We use equivariant localization to construct off-shell entropy functions for supersymmetric black holes in $\mathcal{N}=2$, $D=4$ gauged supergravity coupled to matter. This allows one to compute the black hole entropy without solving the supergravity equations of motion and provides a novel generalization of the attractor mechanism. We consider magnetically charged black holes in $AdS_4$ which have an $AdS_2\times M_2$ near horizon geometry, where $M_2$ is a sphere or a spindle, and we also obtain entropy functions for ungauged supergravity as a simple corollary. We derive analogous results for black strings and rings in $D=5$ supergravity which have an $AdS_3\times M_2$ near horizon geometry, and in this setting we derive an off-shell expression for the central charge of the dual $\mathcal{N}=(0,2)$, $d=2$~SCFT.

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arXiv2024

Equivariant localization for AdS/CFT

We explain how equivariant localization may be applied to AdS/CFT to compute various BPS observables in gravity, such as central charges and conformal dimensions of chiral primary operators, without solving the supergravity equations. The key ingredient is that supersymmetric AdS solutions with an R-symmetry are equipped with a set of equivariantly closed forms. These may in turn be used to impose flux quantization and compute observables for supergravity solutions, using only topological information and the Berline--Vergne--Atiyah--Bott fixed point formula. We illustrate the formalism by considering $AdS_5\times M_6$ and $AdS_3\times M_8$ solutions of $D=11$ supergravity. As well as recovering results for many classes of well-known supergravity solutions, without using any knowledge of their explicit form, we also compute central charges for which explicit supergravity solutions have not been constructed.

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arXiv2023

Localizing Wrapped M5-branes and Gravitational Blocks

We consider $d=2$, $\mathcal{N}=(0,2)$ SCFTs that can arise from M5-branes wrapping four-dimensional, complex, toric manifolds and orbifolds. We use equivariant localization to compute the off-shell central charge of the dual supergravity solutions, obtaining a result which can be written as a sum of gravitational blocks and precisely agrees with a field theory computation using anomaly polynomials and $c$-extremization.

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arXiv2023

Equivariant localization in supergravity

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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arXiv2023

Gravitational Blocks, Spindles and GK Geometry

We derive a gravitational block formula for the supersymmetric action for a general class of supersymmetric AdS solutions, described by GK geometry. Extremal points of this action describe supersymmetric AdS$_3$ solutions of type IIB supergravity, sourced by D3-branes, and supersymmetric AdS$_2$ solutions of $D=11$ supergravity, sourced by M2-branes. In both cases, the branes are also wrapped over a two-dimensional orbifold known as a spindle, or a two-sphere. We develop various geometric methods for computing the gravitational block contributions, allowing us to recover previously known results for various explicit supergravity solutions, and to significantly generalize these results to other compactifications. For the AdS$_3$ solutions we give a general proof that our off-shell supersymmetric action agrees with an appropriate off-shell $c$-function in the dual field theory, establishing a very general exact result in holography. For the AdS$_2$ solutions our gravitational block formula allows us to obtain the entropy for supersymmetric, magnetically charged and accelerating black holes in AdS$_4$.

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