arXiv subjects

Chiara Toldo

Publications and source records attributed to Chiara Toldo.

At least 19 recordsLinked to original sources

arXiv2026

Quantum corrections to the near-extremal thermodynamics of (warped) BTZ black holes

We study one-loop effects in the near-extremal thermodynamics of BTZ and warped BTZ black holes, with particular emphasis on the fate of eigenmodes that become zero modes in the extremal throat. Our analysis is formulated in three-dimensional Topologically Massive Gravity, a higher derivative theory characterized by the presence of a gravitational Chern--Simons term, and it makes use of the Newman--Penrose formulation. For BTZ, we compare the near-horizon computation with the full-geometry eigenvalue problem and identify how the Schwarzian and rotational sectors are lifted at small temperature. We then extend the same strategy to warped BTZ. We find that rotational modes are essential for a consistent near-extremal treatment of both BTZ and warped BTZ black holes, and cannot be discarded without first specifying the boundary conditions.

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arXiv2025

Gravitational dynamics of near-extreme Kerr (Anti-)de Sitter black holes

We analyze the thermodynamic response near extremality of black holes with angular momentum in (3+1)-dimensional de Sitter and Anti-de Sitter spacetimes. While Kerr-AdS$_4$ is characterized by a single extremal limit, for Kerr-dS$_4$ there are three different extremal scenarios (Cold, Nariai and Ultracold). These exhibit different near horizon geometries, with AdS$_2$, dS$_2$ and Mink$_2$ factors respectively. We analyze each extremal case and contrast the response once the black holes are taken out of extremality. We study the perturbations of the near horizon geometry at the level of the 4D metric, considering a consistent truncation for the metric fluctuations, and find solutions to the linearized Einstein equations. We characterize the perturbations that are responsible for the deviations away from extremality and show that their dynamics is governed by a Schwarzian theory. We treat the Ultracold case separately, detailing how the thermodynamics in 4D is reflected in the near horizon dynamics.

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arXiv2025

Quantum corrections to the path integral of near extremal de Sitter black holes

We study quantum corrections to the Euclidean path integral of charged and static four-dimensional de Sitter (dS$_4$) black holes near extremality. These black holes admit three different extremal limits (Cold, Nariai and Ultracold) which exhibit AdS$_2 \times S^2 $, dS$_2 \times S^2 $ and $\text{Mink}_2 \times S^2$ near horizon geometries, respectively. The one-loop correction to the gravitational path integral in the near horizon geometry is plagued by infrared divergencies due to the presence of tensor, vector and gauge zero modes. Inspired by the analysis of black holes in flat space, we regulate these divergences by introducing a small temperature correction in the Cold and Nariai background geometries. In the Cold case, we find a contribution from the gauge modes which is not present in previous work in asymptotically flat spacetimes. Several issues concerning the Nariai case, including the presence of negative norm states and negative eigenvalues, are discussed, together with problems faced when trying to apply this procedure to the Ultracold solution.

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arXiv2024

Mixed 't Hooft Anomalies and the Witten Effect for AdS Black Holes

For a variety of BPS black holes in string theory, the supersymmetric index has provided a microscopic validation of the Bekenstein-Hawking formula. In the near-BPS limit, a gravitational path integral analysis previously revealed the semiclassical spectrum is modified, having a large extremal degeneracy (consistent with the index) and a mass gap up to a continuum of non-BPS black holes. Presently, we study examples in which these sharp features of the spectrum are altered due to the presence of anomalies in the form of $\vartheta$-angle terms in the action. These may appear generally, but we focus on near-BPS dyonic AdS$_4$ black holes in M-theory, dual to 3d $\mathcal{N}=2$ SCFTs of Class $R$ obtained by twisted compactification of $N$ wrapped M5 branes. Due to the Witten effect, the dyonic black holes receive quantum corrections to their charges, and when $\vartheta = \pi$ one may find a mixed `t Hooft anomaly between the $U(1)_R$ and $\mathbb{Z}_2$ time reversal symmetries. Using results from $\mathcal{N}=2$ JT supergravity, we find these effects result in a spectrum in which both the gap and index are reduced, and may even vanish. Surprisingly, for $\vartheta \rightarrow \pi$, neither the Bekenstein-Hawking formula nor the index correctly account for the extremal degeneracies.

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arXiv2024

The spectrum of near-BPS Kerr-Newman black holes and the ABJM mass gap

Supersymmetric rotating 1/16-BPS black holes in $AdS_4 \times S^7$ are expected to capture the average degeneracy of BPS states in the dual ABJM superconformal theory for given fixed charges. This has been successfully demonstrated for the superconformal index using complexified black hole metrics, but a naive Gibbons-Hawking calculation of the actual degeneracies in the low temperature limit is invalid due to large quantum fluctuations of the near horizon $AdS_2$ metric. We argue that in a particular mixed grand/canonical ensemble, these fluctuations of the near-BPS Kerr-Newman black holes are described by a version of the $\mathcal{N}=2$ super-Schwarzian theory with $SU(1,1|1)$ symmetry. Using this description as well as properties of ABJM, we recover the large $N$ superconformal index and find a characteristic ``mass gap'' of order $N^{-3/2}$ between the 1/16-BPS states and the lightest near BPS state. We further make a prediction for the operator dimension spectrum above the gap in the large $N$, low $T$ limit. Our results are consistent with the Bekenstein-Hawking formula at large energies, random matrix theory at low energies, and the microscopic index.

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arXiv2024

Quasinormal Corrections to Near-Extremal Black Hole Thermodynamics

Recent work on the quantum mechanics of near-extremal non-supersymmetric black holes has identified a characteristic $T^{3/2}$ scaling of the low temperature black hole partition function. This result has only been derived using the path integral in the near-horizon region and relies on many assumptions. We discuss how to derive the $T^{3/2}$ scaling for the near-extremal rotating BTZ black hole from a calculation in the full black hole background using the Denef-Hartnoll-Sachdev (DHS) formula, which expresses the 1-loop determinant of a thermal geometry in terms of a product over the quasinormal mode spectrum. We also derive the spectral measure for fields of any spin in Euclidean BTZ and use it to provide a new proof of the DHS formula and a new, direct derivation of the BTZ heat kernel. The computations suggest a path to proving the $T^{3/2}$ scaling for the asymptotically flat 4d Kerr black hole.

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arXiv2023

Logarithmic Corrections to Kerr Thermodynamics

Recent work has shown that loop corrections from massless particles generate $\frac{3}{2}\log T_{\text{Hawking}}$ corrections to black hole entropy which dominate the thermodynamics of cold near-extreme charged black holes. Here we adapt this analysis to near-extreme Kerr black holes. Like AdS$_2\times S^2$, the Near-Horizon Extreme Kerr (NHEK) metric has a family of normalizable zero modes corresponding to reparametrizations of boundary time. The path integral over these zero modes leads to an infrared divergence in the one-loop approximation to the Euclidean NHEK partition function. We regulate this divergence by retaining the leading finite temperature correction in the NHEK scaling limit. This "not-NHEK" geometry lifts the eigenvalues of the zero modes, rendering the path integral infrared finite. The quantum-corrected near-extremal entropy exhibits $\frac{3}{2}\log T_{\text{Hawking}}$ behavior characteristic of the Schwarzian model and predicts a lifting of the ground state degeneracy for the extremal Kerr black hole.

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arXiv2023

Magnetic charge and black hole supersymmetric quantum statistical relation

We study the thermodynamics in the BPS limit of AdS black holes realizing the topological twist. We use a limiting procedure that allows us to reach the extremal point along a trajectory in the space of supersymmetric Euclidean solutions. We show that on this space we can write a quantum statistical relation, which is well-defined in the BPS limit and relies on imposing a suitable constraint among the chemical potentials, due to supersymmetry and regularity. We stress the importance of this in relating the thermal partition function of the dual field theory to the topologically twisted index.

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arXiv2023

Near-Extremal Limits of de Sitter Black Holes

We analyze the thermodynamic response near extremality of charged black holes in four-dimensional Einstein-Maxwell theory with a positive cosmological constant. The latter exhibit three different extremal limits, dubbed cold, Nariai and ultracold configurations, with near-horizon geometries AdS$_2 \times S^2$, dS$_2 \times S^2$, Mink$_2 \times S^2$, respectively. For each of these three cases we analyze small deformations away from extremality, and contrast their response. We also construct the effective two-dimensional theory, obtained by dimensional reduction, that captures these features and we provide a more detailed analysis of the perturbations around the near-horizon geometry for each case. Our results for the ultracold case in particular show an interesting interplay between the entropy variation and charge variation, realizing a different symmetry breaking with respect to the other two near-extremal limits.

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arXiv2021

On the Search for Multicenter AdS Black Holes from M-theory

We study the effective potentials for various probe branes surrounding AdS$_4$ black holes with massive halos in consistent truncations of M-theory on the Sasaki-Einstein$_7$ manifolds $Q^{111}$ and $M^{111}$. These probes are either M2 branes extended in spacetime or "particle-like" probes such as internally wrapped M2 branes and, upon reduction to type IIA string theory, D6 branes corresponding to baryon operators in the dual Chern-Simons theory. We find both global and local minima of the potential outside the horizon, indicating the existence of stable and metastable multicenter AdS black holes in the extreme mass ratio regime, at fixed temperature and charges. For the planar case, we also find an instability towards nucleation of spacetime-filling M2 branes. With this analysis, we address some open questions on the holographic description of glassy phases of matter.

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arXiv2021

Rotating 5D Black Holes: Interactions and deformations near extremality

We study a two-dimensional theory of gravity coupled to matter that is relevant to describe holographic properties of black holes with a single rotational parameter in five dimensions (with or without cosmological constant). We focus on the near-horizon geometry of the near-extremal black hole, where the effective theory reduces to Jackiw-Teitelboim (JT) gravity coupled to a massive scalar field. We compute the corrections to correlation functions due to cubic interactions present in this theory. A novel feature is that these corrections do not have a definite sign: for AdS$_5$ black holes the sign depends on the mass of the extremal solution. We discuss possible interpretations of these corrections from a gravitational and holographic perspective. We also quantify the imprint of the JT sector on the UV region, i.e. how these degrees of freedom, characteristic for the near-horizon region, influence the asymptotically far region of the black hole. This gives an interesting insight on how to interpret the IR modes in the context of their UV completion, which depends on the environment that contains the black hole.

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arXiv2021

Bounds on multiscalar CFTs in the epsilon expansion

We study fixed points with N scalar fields in $4 - \varepsilon$ dimensions to leading order in $\varepsilon$ using a bottom-up approach. We do so by analyzing O(N) invariants of the quartic coupling $λ_{ijkl}$ that describes such CFTs. In particular, we show that $λ_{iijj}$ and $λ_{ijkl}^2$ are restricted to a specific domain, refining a result by Rychkov and Stergiou. We also study averages of one-loop anomalous dimensions of composite operators without gradients. In many cases, we are able to show that the O(N) fixed point maximizes such averages. In the final part of this work, we generalize our results to theories with N complex scalars and to bosonic QED. In particular we show that to leading order in $\varepsilon$, there are no bosonic QED fixed points with N < 183 flavors.

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arXiv2020

Holographic duals of refined partition functions

Recent years have witnessed lots of progress in the computation of supersymmetric partition functions of SCFTs on curved manifolds via localization. The twisted partition function on product manifolds of the form $S^1 \times Σ_g$, where $Σ_g$ is a two-dimensional Riemann surface, is of particular relevance due to its role in the microstate counting for magnetic static AdS$_4$ black holes realizing the topological twist. We review here supergravity solutions having as conformal boundary more general 3d manifolds. We first focus on solutions (AdS-Taub-NUT and AdS-Taub-Bolt) having as boundary a circle bundle over $Σ_g$, showing the matching of their on-shell action with the large $N$ limit of the partition function of the dual CFT. We then discuss some recent results for a challenging example, which involves the refinement by angular momentum. The gravitational backgrounds in this case are rotating supersymmetric AdS$_4$ black holes. We review the salient features of two different classes of such solutions in theories of supergravity with uplift in M-theory, and comment on the current status of their entropy counting in the dual CFT.

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arXiv2019

Supersymmetric Rényi entropy and charged hyperbolic black holes

The supersymmetric Rényi entropy across a spherical entangling surface in a $d$-dimensional SCFT with flavor defects is equivalent to a supersymmetric partition function on $\mathbb{H}^{d-1} \times \mathbb{S}^1$, which can be computed exactly using localization. We consider the holographically dual BPS solutions in $(d +1)$-dimensional matter coupled supergravity $(d = 3 , 5)$, which are charged hyperbolically sliced AdS black holes. We compute the renormalized on-shell action and the holographic supersymmetric Rényi entropy and show a perfect match with the field theory side. Our setup allows a direct map between the chemical potentials for the global symmetries of the field theories and those of the gravity solutions. We also discuss a simple case where angular momentum is added.

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arXiv2019

Rotating attractors and BPS black holes in $AdS_4$

We analyze stationary BPS black hole solutions to 4d $\mathcal{N}=2$ abelian gauged supergravity. Using an appropriate near horizon ansatz, we construct rotating attractors with magnetic flux realizing a topological twist along the horizon surface, for any theory with a symmetric scalar manifold. An analytic flow to asymptotically locally $AdS_4$ is presented for a subclass of these near horizon geometries, and an explicit new example of supersymmetric $AdS_4$ rotating black hole is discussed in detail. We further note that, upon tuning the gauging to special values, one can obtain solutions with different asymptotics, and in particular reductions of doubly spinning asymptotically $AdS_5$ black holes. Finally we present a proposal for the form of the BPS entropy function with rotation, which we expect to be holographically related to the refined twisted index of the dual theory.

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arXiv2019

Matter-coupled supersymmetric Kerr-Newman-AdS$_4$ black holes

We present new analytic rotating AdS$_4$ black holes, found as solutions of 4d gauged $\mathcal{N}=2$ supergravity coupled to abelian vector multiplets with a symmetric scalar manifold. These configurations preserve two real supercharges and have a smooth limit to the BPS Kerr-Newman-AdS$_4$ black hole. We spell out the solution of the $STU$ model admitting an uplift to M-theory on S$^7$. We identify an entropy function, which upon extremization gives the black hole entropy, to be holographically reproduced by the leading $N$ contribution of the generalized superconformal index of the dual theory.

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arXiv2018

Partition functions on 3d circle bundles and their gravity duals

The partition function of a three-dimensional $\mathcal{N} =2$ theory on the manifold $\mathcal{M}_{g,p}$, an $S^1$ bundle of degree $p$ over a closed Riemann surface $Σ_g$, was recently computed via supersymmetric localization. In this paper, we compute these partition functions at large $N$ in a class of quiver gauge theories with holographic M-theory duals. We provide the supergravity bulk dual having as conformal boundary such three-dimensional circle bundles. These configurations are solutions to $\mathcal{N}=2$ minimal gauged supergravity and pertain to the class of Taub-NUT-AdS and Taub-Bolt-AdS preserving $1/4$ of the supersymmetries. We discuss the conditions for the uplift of these solutions to M-theory, and compute the on-shell action via holographic renormalization. We show that the uplift condition and on-shell action for the Bolt solutions are correctly reproduced by the large $N$ limit of the partition function of the dual superconformal field theory. In particular, the $Σ_g \times S^1 \cong \mathcal{M}_{g,0}$ partition function, which was recently shown to match the entropy of $AdS_4$ black holes, and the $S^3 \cong \mathcal{M}_{0,1}$ free energy, occur as special cases of our formalism, and we comment on relations between them.

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arXiv2018

Deforming black holes in AdS

We investigate how changes in the boundary metric affect the shape of AdS black holes. Most of our work is analytic and based on the AdS C-metric. Both asymptotically hyperbolic and compact black holes are studied. It has recently been shown that the AdS C-metric contains configurations of highly deformed black holes, and we show that these deformations are usually the result of similar deformations of the boundary metric. However, quite surprisingly, we also find cases where the horizon is insensitive to certain large changes in the boundary geometry. This motivates the search for a new family of black hole solutions with the same boundary geometry in which the horizon does respond to the changes in the boundary. We numerically construct these solutions and we (numerically) explore how the horizon response to boundary deformations depends on temperature.

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