arXiv subjects

Enrico Turetta

Publications and source records attributed to Enrico Turetta.

9 recordsLinked to original sources

arXiv2026

Decoupling saddles of the gravitational index and the Farey tail

We first construct general saddles of the five-dimensional gravitational supersymmetric index with $S^1\times\mathbb{R}^4$ asymptotics, carrying an arbitrary number of electric charges and Gibbons-Hawking centers. We then uplift the three-charge configurations to type IIB supergravity, obtaining solutions asymptotic to $S^1\times \mathbb{R}^4\times S^1\times {\rm K}3$, carrying D1-D5-P charges. Upon taking a decoupling limit, these solutions yield asymptotically Euclidean AdS$_3\times S^3\times {\rm K}3$ candidate saddles of the dual CFT$_2$ elliptic genus. We focus on the two-center saddles, which involve three integers specifying an orbifold action. Depending on these integers, the saddles may or may not possess a Euclidean horizon, and may be smooth or exhibit orbifold singularities. We give the on-shell action of these two-center saddles in the appropriate ensemble and establish a precise match with the Farey-tail expansion of the elliptic genus. The horizonless saddles are the Euclidean version of fractional spectral-flow solutions previously discussed in the literature, corresponding to $({\rm AdS}_3\times S^3)/\mathbb{Z}_k$ orbifolds. The black hole saddles are modular images of the horizonless ones. They generalize the well-known ${\rm SL}(2,\mathbb{Z})$ family of BTZ black holes by placing it in the background of the $\mathbb{Z}_k$ orbifold. We also consider the asymptotically AdS$_3\times S^3$ solutions arising as decoupling limit of five-dimensional black ring and black lens saddles, provide their on-shell action and confirm that they do not contribute to the D1-D5 elliptic genus.

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arXiv2026

The black hole at the end of the cone: localizing the anomaly polynomial on toric geometries

We consider five-dimensional supergravity coupled to vector multiplets, gauged or ungauged, and propose an efficient method to evaluate the on-shell action of supersymmetric black saddle solutions with toric ${\rm U}(1)^3$ symmetry and general topology, explicitly known or just assumed to exist, including higher-derivative corrections. This is equivalent to equivariant integration of the anomaly polynomial six-form over simplicial cones obtained by decomposing the toric diagram of the solution. The on-shell action is then expressed as a sum over contributions localized at the tip of each cone. We obtain a simple derivation of recently calculated expressions as well as new predictions, both for the on-shell action of the black saddles and the Wald entropy of the related extremal solutions. These may be asymptotically AdS$_5$ or asymptotically flat. As examples, we discuss black holes, black rings and black lenses, including a black hole in the background of a topological soliton.

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arXiv2026

Black holes from the gravitational path integral: supersymmetric indices and precision holography

The counting of microstates of supersymmetric black holes with anti-de Sitter or flat asymptotics is obtained by computing a supersymmetric index in a weakly coupled string theory or a dual superconformal field theory. These indices are protected observables, whose value can be reliably extrapolated from weak to strong coupling, where the gravitational description applies. In this Thesis, after a broad introductory review, we discuss recent progress in formulating such protected observables directly within the gravitational theory, via the Euclidean path integral. In the semiclassical limit the index reduces to a sum over complex Euclidean saddles. These saddles are supersymmetric but ''non-extremal'', and arise in both anti-de Sitter and flat spaces. In the holographic setting, we investigate four-derivative corrections to the thermodynamics of AdS$_5$ black holes. Using off-shell methods, we construct the corrected action of five-dimensional gauged supergravity. We then evaluate the corrected on-shell action of supersymmetric AdS$_5$ black holes and find exact agreement with a Cardy-like limit of the superconformal index of the dual conformal field theory. By a Legendre transform of the action, we obtain the corrected black hole entropy, and we confirm this result by applying Wald's formula to the corrected near-horizon geometry. We then turn to the gravitational index with asymptotically flat boundary conditions. We uncover a broad family of novel saddles and present a general classification based on their rod structure, which characterizes their topology. These solutions may feature multiple horizons or three-dimensional bubbles with lens space topology, and allowing for conical singularities yields further geometries, involving spindles and branched spheres. For the simpler geometries, the on-shell action is computed using an odd-dimensional version of equivariant localization.

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arXiv2025

Bubbling saddles of the gravitational index

We consider the five-dimensional supergravity path integral that computes a supersymmetric index, and uncover a wealth of semiclassical saddles with bubbling topology. These are complex finite-temperature configurations asymptotic to $S^1\times\mathbb{R}^4$, solving the supersymmetry equations. We assume a ${\rm U}(1)^3$ symmetry given by the thermal isometry and two rotations, and present a general construction based on a rod structure specifying the fixed loci of the ${\rm U}(1)$ isometries and their three-dimensional topology. These fixed loci may correspond to multiple horizons or three-dimensional bubbles, and they may have $S^3$, $S^2\times S^1$, or lens space topology. Allowing for conical singularities gives additional topologies involving spindles and branched spheres or branched lens spaces. As a particularly significant example, we analyze in detail the configurations with a horizon and a bubble just outside of it. We determine the possible saddle-point contribution of these configurations to the gravitational index by evaluating their on-shell action and the relevant thermodynamic relations. We also spell out two limits leading to well-defined Lorentzian solutions. The first is the extremal limit, which gives the known BPS black ring and black lens solutions. The on-shell action and chemical potentials remain well-defined in this limit and should thus provide the contribution of the black ring and black lens to the gravitational index. The second is a limit leading to horizonless bubbling solutions, which have purely imaginary action.

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arXiv2025

Three-charge black holes from the worldsheet

We consider the general asymptotically flat, doubly-rotating, three-charge black hole uplifted to a family of NS5-F1-P black brane solutions of Type IIB supergravity. We construct a null-gauged WZW model whose target-space geometry reproduces this background in the NS5 decoupling limit, and show that the gauging parameters precisely satisfy the appropriate consistency conditions on the perturbative string spectrum. Through an analytic continuation and an appropriate limit, this model relates to a recently studied construction describing strings on smooth, horizonless geometries. We further analyze the supersymmetric and extremal three-charge configuration, corresponding to the ten-dimensional uplift of the (NS5-decoupled) BMPV black hole, and show that it requires a novel class of null-gauged WZW models. Our construction provides explicit examples of worldsheet CFTs that capture string dynamics on certain black hole geometries with linear dilaton asymptotics.

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arXiv2024

Localization of the 5D supergravity action and Euclidean saddles for the black hole index

We investigate equivariant localization of the gravitational on-shell action in odd dimensions, focusing on five-dimensional ungauged supergravity. We analyze the conditions for cancellation of boundary terms, so that the full action integral is given in terms of the odd-dimensional analog of the nuts and bolts of Gibbons-Hawking. We specialize to supersymmetric configurations with an additional ${\rm U}(1)$ symmetry preserving the supercharge and provide a formula for the localized on-shell action. We construct asymptotically flat Euclidean supersymmetric non-extremal solutions with two independent rotations and an arbitrary number of electric charges, providing black hole saddles of the gravitational path integral that computes a supersymmetric index, and evaluate their action equivariantly. We find that these Euclidean saddles interpolate between supersymmetric extremal black holes and two-center horizonless microstate geometries. The interpolation involves dialing the temperature and implementing different analytic continuations. The corresponding on-shell action does not depend on temperature but is affected by the analytic continuations.

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arXiv2024

Higher-derivative corrections to flavoured BPS black hole thermodynamics and holography

A Cardy-like regime of the four-dimensional superconformal index has been shown to be governed by 't Hooft anomalies and to single out a large-$N$ saddle carrying the Bekenstein-Hawking entropy of dual supersymmetric black holes in AdS$_5$. For the universal index where no flavour fugacities are turned on, this correspondence has been improved by matching the first subleading corrections to the saddle-point action with the four-derivative corrections to the black hole action in minimal gauged supergravity, as well as the respective corrected entropies. Here, we extend this match by including flavour symmetries. We consider five-dimensional gauged supergravity with vector multiplet and four-derivative couplings, and provide an effective theory reproducing the 't Hooft anomalies of the R- and flavour symmetries of generic holographic superconformal field theories at next-to-leading order in the large-$N$ expansion. Then we focus on a specific model dual to $\mathbb{C}^3/\mathbb{Z}_ν$ quiver gauge theories, where the 't Hooft anomaly coefficients receive simple but sufficiently generic corrections. In this model, we evaluate the four-derivative corrections to the on-shell action of the supersymmetric multi-charge black hole, showing agreement with the flavoured Cardy-like formula from the index. We give a prediction for the corrected entropy of the supersymmetric black hole and discuss the general validity of our results. Taking the limit of infinite AdS$_5$ radius, we also obtain four-derivative corrections to the action and entropy of supersymmetric asymptotically flat black holes.

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arXiv2023

Boundary terms and conserved charges in higher-derivative gauged supergravity

We address some issues in higher-derivative gauged supergravity with Chern-Simons terms, focusing on the five-dimensional case. We discuss the variational problem with Dirichlet boundary conditions as well as holographic renormalization in asymptotically locally AdS spacetimes, and derive the corresponding boundary terms. We then employ Wald's formalism in order to define conserved charges associated to local symmetries (diffeomorphisms and U(1) gauge transformations), taking into account the effect of generic gauge Chern-Simons terms. We prove that the first law of black hole mechanics and the quantum statistical relation hold in this setup. Chern-Simons terms also lead us to distinguish between Noether charges and Page (or Komar) charges which satisfy the Gauss law. We make use of the latter to compute corrections to the angular momentum and electric charge of the supersymmetric black hole in AdS$_5$ from its corrected near-horizon geometry. This also allows us to derive the microcanonical form of the entropy as a function of the conserved charges relying entirely on the near-horizon geometry. Finally, we comment on four-derivative gauged supergravity in four dimensions, showing that field redefinitions permit to simplify the action at linear order in the corrections, so that the equations of motion are those of the two-derivative theory.

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arXiv2022

Corrections to AdS$_5$ Black Hole Thermodynamics from Higher-Derivative Supergravity

We study four-derivative corrections to five-dimensional minimal gauged supergravity. We evaluate the on-shell action of the AdS$_5$ black hole solution with two independent angular momenta and one electric charge at linear order in the corrections. After imposing supersymmetry, we are able to recast the action in terms of the supersymmetric chemical potentials and match the result obtained from the dual superconformal index on the second sheet. To achieve this, we exploit the freedom to implement field redefinitions to recast the action in a much simpler form, as well as the fact that the two-derivative solution is enough. We use the on-shell action to determine the corrections to the black hole thermodynamics, including those to the entropy and the charges. We then specialize to the supersymmetric and extremal case and find a simple expression for the microcanonical entropy. In particular, for the case with one independent angular momentum the corrections are entirely encoded in the dual superconformal anomaly coefficients. We corroborate this result for the entropy by constructing the corrected near-horizon solution and applying Wald's formula.

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