We consider supersymmetric solutions of $\textit{D}$ = 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 $\textit{ℓ}$. Using $\textit{ℓ}$ to perform a dimensional reduction to $\textit{D}$ = 4, $$ \mathcal{N} $$ = 2 gauged supergravity, we show how the $\textit{D}$ = 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.

Switzerland

Pietro Genolini

United Kingdom

Jerome Gauntlett

Yusheng Jiao

Jaeha Park

James Sparks

Equivariant localization for $\textit{D}$ = 5 gauged supergravity

We use equivariant localization and holography to study four-dimensional $$ \mathcal{N}=1 $$ superconformal field theories arising from M5-branes wrapped on a punctured Riemann surface. We explain how, given a Riemann surface with marked points, one can glue in a “puncture geometry” locally around each point. Using equivariant localization we show that the central charge consists of a bulk contribution plus localized puncture contributions. We recover and generalize the known results for locally $$ \mathcal{N}=2 $$ preserving punctures, and derive new results for genuinely locally $$ \mathcal{N}=1 $$ preserving punctures.

Christopher Couzens

Alice Lüscher

Localizing punctures in M-theory

We derive a general formula for the on-shell action of six-dimensional Euclidean Romans supergravity using equivariant localization. Our results are obtained without the need for solving any of the equations of motion, instead working on the assumption of the existence of a supersymmetric solution. We show that the on-shell action is completely determined in terms of the R-symmetry Killing vector and topological data. We easily recover known results in the literature, make predictions for hitherto unknown solutions, and also match to holographic field theory duals.

Brazil

Carolina Gregory

Davide Muniz

Tabea Sieper

Localizing Romans supergravity

We consider supersymmetric solutions of $\textit{D}$ = 4, $$ \mathcal{N} $$ = 2 Euclidean gauged supergravity coupled to an arbitrary number of vector multiplets. Such solutions admit an R-symmetry Killing vector, $\textit{ξ}$, 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 d = d – $\textit{ξ}$⌟ . 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 be ever constructed in closed form.

Equivariant localization for $\textit{D}$ = 4 gauged supergravity

<p>We introduce a general class of toric gravitational instantons in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mo>=</mo><mn>4</mn></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>2</mn></math> gauged supergravity, namely Euclidean supersymmetric solutions with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msup><mo stretchy="false">)</mo><mn>2</mn></msup></math> isometry. Such solutions are specified by a “supergravity labeled polytope,” where the labels encode the four-manifold topology, the choice of magnetic fluxes, and certain signs associated with the Killing spinor. Equivariant localization 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 <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> field theories are defined on the boundary three-manifolds, which are (squashed) lens spaces <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>L</mi><mo stretchy="false">(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo stretchy="false">)</mo></math> or generalizations with orbifold singularities.</p>

Pietro Benetti Genolini

Jerome P. Gauntlett

Toric gravitational instantons in gauged supergravity

<p>Dark matter particles with a mass around 1 eV can decay into near-infrared photons. Utilizing available public blank sky observations from the NIRSpec IFU on the James Webb Space Telescope (JWST), we search for a narrow emission line due to decaying dark matter and derive leading constraints in the mass range 0.8–3 eV on the decay rate to photons, and more specifically, on the axion-photon coupling for the case of axionlike particles. We exclude <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>τ</mi><mo>&lt;</mo><mn>3.5</mn><mo>×</mo><msup><mn>10</mn><mn>26</mn></msup><mtext> </mtext><mtext> </mtext><mi mathvariant="normal">s</mi></math> at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>m</mi></mrow><mrow><mi>DM</mi></mrow></msub><mo>≃</mo><mn>0.8</mn><mtext> </mtext><mtext> </mtext><mi>eV</mi></mrow></math> and, in the case of axions, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>g</mi></mrow><mrow><mi>a</mi><mi>γ</mi><mi>γ</mi></mrow></msub><mo>&gt;</mo><mn>1.3</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>11</mn></mrow></msup><mtext> </mtext><mtext> </mtext><msup><mrow><mi>GeV</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math> for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>m</mi></mrow><mrow><mi>a</mi></mrow></msub><mo>≃</mo><mn>2.2</mn><mtext> </mtext><mtext> </mtext><mi>eV</mi></mrow></math>. Our results do not rely on dedicated observations, rather we use blank sky observations intended for sky subtraction, and thus our reach may be automatically strengthened as JWST continues to observe.</p>

United States

Ryan Janish

Elena Pinetti

Hunting Dark Matter Lines in the Infrared Background with the James Webb Space Telescope

We derive a general formula for the gravitational free energy of Euclidean supersymmetric solutions to <math><mrow><mi>D</mi><mo>=</mo><mn>4</mn></mrow></math>, <math><mi>N</mi><mo>=</mo><mn>2</mn></math> 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.

Localization of the Free Energy in Supergravity

Supersymmetric, magnetically charged (and possibly accelerating) black holes in AdS4 that uplift on Sasaki-Einstein manifolds Y 7 to M-theory have a dual matrix model description. The matrix model in turn arises by localization of the 3d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 SCFTs, dual to the AdS4 vacuum, on the black hole horizon geometry, which is a Riemann surface Σ g  (or a spindle Σ). We identify the imaginary part t of the continuously distributed eigenvalues in the matrix model, and their density function ρ(t), with natural geometric quantities associated with the M-theory circle action U(1) M  on the near-horizon geometry AdS2 × Y 9, the internal space Y 9 being a Y 7 fibration over Σ g  (or Σ). Moreover, we argue that the points where ρ  ′ (t) is discontinuous match with the classical action of BPS probe M2-branes wrapping AdS2 and the M-theory circle. We illustrate our findings with the ABJM and ADHM theories, whose duals have Y 7 = S 7/ℤ  k , and some of their flavoured variants corresponding to other toric Y 7.

Andrea Boido

Matrix models from black hole geometries

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 × 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 × 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.

Localization and attraction

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 × M 6 and AdS 3 × 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.