arXiv subjects

Alejandra Castro

Publications and source records attributed to Alejandra Castro.

At least 37 records · Page 2Linked to original sources

arXiv2021

Gravitational perturbations from NHEK to Kerr

We revisit the spectrum of linear axisymmetric gravitational perturbations of the (near-)extreme Kerr black hole. Our aim is to characterise those perturbations that are responsible for the deviations away from extremality, and to contrast them with the linearized perturbations treated in the Newman-Penrose formalism. For the near horizon region of the (near-)extreme Kerr solution, i.e. the (near-)NHEK background, we provide a complete characterisation of axisymmetric modes. This involves an infinite tower of propagating modes together with the much subtler low-lying mode sectors that contain the deformations driving the black hole away from extremality. Our analysis includes their effects on the line element, their contributions to Iyer-Wald charges around the NHEK geometry, and how to reconstitute them as gravitational perturbations on Kerr. We present in detail how regularity conditions along the angular variables modify the dynamical properties of the low-lying sector, and in particular their role in the new developments of nearly-AdS$_2$ holography.

hep-th↗

arXiv2021

A note on the $\mathcal{N}=2$ super-$\mathcal{W}_3$ holographic dictionary

This is a long-overdue companion paper to arXiv:1512.00073. We study the relation between $sl(3|2)$ Chern-Simons supergravity on AdS$_3$ and two-dimensional CFT's with $\mathcal{N}=2$ super-$\mathcal{W}_3$ symmetry. Specifically, we carry out a complete analysis of asymptotic symmetries in a basis that makes the superconformal structure transparent, allowing us to establish the precise dictionary between currents and transformation parameters in the bulk and their boundary counterparts. We also discuss the incorporation of sources and display in full detail the corresponding holographic Ward identities. By imposing suitable hermiticity conditions on the CFT currents, we identify the superalgebra $su(2,1|1,1)$ as the appropriate real form of $sl(3|2)$ in Lorentzian signature. We take the opportunity to review some of the properties of the $\mathcal{N}=2$ super-$\mathcal{W}_3$ conformal algebra, including its multiplet structure, OPE's and spectral flow invariance, correcting some minor typos present in the literature.

hep-th↗

arXiv2020

$\mathcal{N}=2$ Minimal Models: A Holographic Needle in a Symmetric Orbifold Haystack

We explore large-$N$ symmetric orbifolds of the $\mathcal N=2$ minimal models, and find evidence that their moduli spaces each contain a supergravity point. We identify single-trace exactly marginal operators that deform them away from the symmetric orbifold locus. We also show that their elliptic genera exhibit slow growth consistent with supergravity spectra in AdS$_3$. We thus propose an infinite family of new holographic CFTs.

hep-th↗

arXiv2020

Gravitational Wilson Lines in 3D de Sitter

We construct local probes in the static patch of Euclidean dS$_3$ gravity. These probes are Wilson line operators, designed by exploiting the Chern-Simons formulation of 3D gravity. Our prescription uses non-unitary representations of $so(4)\simeq su(2)_L\times su(2)_R$, and we evaluate the Wilson line for states satisfying a singlet condition. We discuss how to reproduce the Green's functions of massive scalar fields in dS$_3$, the construction of bulk fields, and the quasinormal mode spectrum. We also discuss the interpretation of our construction in Lorentzian signature in the inflationary patch, via $SL(2,\mathbb{C})$ Chern-Simons theory.

hep-th↗

arXiv2020

Gravitational Anomalies in nAdS$_2$/nCFT$_1$

We revisit the holographic description of the near horizon geometry of the BTZ black hole in AdS$_3$ gravity, with a gravitational Chern-Simons term included. After a dimensional reduction of the three dimensional theory, we use the framework of nAdS$_2$/nCFT$_1$ to describe the near horizon physics. This setup allows us to contrast the role of the gravitational and conformal anomaly inherited from AdS$_3$/CFT$_2$ in the symmetry breaking mechanism of nAdS$_2$/nCFT$_1$. Our results display how boundary conditions in the 3D spacetime, combined with the gravitational anomaly, affect the holographic description of the near horizon of the black hole relative to the physics near the AdS$_3$ boundary.

hep-th↗

arXiv2020

Wilson Lines and Ishibashi States in AdS$_3$/CFT$_2$

We provide a refined interpretation of a gravitational Wilson line in AdS$_3$ in terms of Ishibashi states in the dual CFT$_2$. Our strategy is to give a method to evaluate the Wilson line that accounts for all the information contained in the representation, and clarify the role of boundary conditions at the endpoints of the line operator. This gives a novel way to explore and reconstruct the local bulk dynamics which we discuss. We also compare our findings with other interpretations of Ishibashi states in AdS$_3$/CFT$_2$.

hep-th↗

arXiv2020

The Holographic Landscape of Symmetric Product Orbifolds

We investigate the growth of coefficients in the elliptic genus of symmetric product orbifolds at large central charge. We find that this landscape decomposes into two regions. In one region, the growth of the low energy states is Hagedorn, which indicates a stringy dual. In the other, the growth is much slower, and compatible with the spectrum of a supergravity theory on AdS$_3$. We provide a simple diagnostic which places any symmetric product orbifold in either region. We construct a class of elliptic genera with such supergravity-like growth, indicating the possible existence of new realizations of AdS$_3$/CFT$_2$ where the bulk is a semi-classical supergravity theory. In such cases, we give exact expressions for the BPS degeneracies, which could be matched with the spectrum of perturbative states in a dual supergravity description.

hep-th↗

arXiv2019

Warped Symmetries of the Kerr Black Hole

We propose a set of diffeomorphism that act non-trivially near the horizon of the Kerr black hole. We follow the recent developments of Haco-Hawking-Perry-Strominger to quantify this phase space, with the most substantial difference being our choice of vectors fields. Our gravitational charges are organized into a Virasoro-Kac-Moody algebra with non-trivial central extensions. We interpret this algebra as arising from a warped conformal field theory. Using the data we can infer from this warped CFT description, we capture the thermodynamic properties of the Kerr black hole.

hep-th↗

arXiv2019

Breaking away from the near horizon of extreme Kerr

We study gravitational perturbations around the near horizon geometry of the (near) extreme Kerr black hole. By considering a consistent truncation for the metric fluctuations, we obtain a solution to the linearized Einstein equations. The dynamics is governed by two master fields which, in the context of the nAdS$_2$/nCFT$_1$ correspondence, are both irrelevant operators of conformal dimension $Δ=2$. These fields control the departure from extremality by breaking the conformal symmetry of the near horizon region. One of the master fields is tied to large diffeomorphisms of the near horizon, with its equations of motion compatible with a Schwarzian effective action. The other field is essential for a consistent description of the geometry away from the horizon.

hep-th↗

arXiv2019

Siegel Paramodular Forms from Exponential Lifts: Slow versus Fast Growth

We investigate the growth of Fourier coefficients of Siegel paramodular forms built by exponentially lifting weak Jacobi forms, focusing on terms with large negative discriminant. To this end we implement a method based on deforming contours that expresses the coefficients of all such terms as residues. We find that there are two types of weak Jacobi forms, leading to two different growth behaviors: the more common type leads to fast, exponential growth, whereas a second type leads to slower growth, akin to the growth seen in ratios of theta functions. We give a simple criterion to distinguish between the two types, and give a simple closed form expression for the coefficients in the slow growing case. In a companion article [1], we provide physical applications of these results to symmetric product orbifolds and holography.

hep-th↗

arXiv2019

Siegel Paramodular Forms and Sparseness in AdS$_3$/CFT$_2$

We discuss the application of Siegel paramodular forms to the counting of polar states in symmetric product orbifold CFTs. We present five special examples and provide exact analytic counting formulas for their polar states. The first example reproduces the known result for type IIB supergravity on AdS$_3\times S^3\times K3$, whereas the other four examples give new counting formulas. Their crucial feature is that the low energy spectrum is very sparse, which suggests the existence of a suitable dual supergravity theory. These examples open a path to novel realizations of AdS$_3$/CFT$_2$.

hep-th↗

arXiv2019

5D Rotating Black Holes and the nAdS$_2$/nCFT$_1$ Correspondence

We study rotating black holes in five dimensions using the nAdS$_2$/nCFT$_1$ correspondence. A consistent truncation of pure Einstein gravity (with a cosmological constant) in five dimensions to two dimensions gives a generalization of the Jackiw-Teitelboim theory that has two scalar fields: a dilaton and a squashing parameter that breaks spherical symmetry. The interplay between these two scalar fields is non trivial and leads to interesting new features. We study the holographic description of this theory and apply the results to the thermodynamics of the rotating black hole from a two dimensional point of view. This setup challenges notions of universality that have been advanced based on simpler models: we find that the mass gap of Kerr-AdS$_5$ corresponds to an undetermined effective coupling in the nAdS$_2$/nCFT$_1$ theory which depends on ultraviolet data.

hep-th↗

arXiv2018

Logarithmic Corrections to Black Hole Entropy: the Non-BPS Branch

We compute the leading logarithmic correction to black hole entropy on the non-BPS branch of 4D ${\cal N}\geq 2$ supergravity theories. This branch corresponds to finite temperature black holes whose extremal limit does not preserve supersymmetry, such as the $D0-D6$ system in string theory. Starting from a black hole in minimal Kaluza-Klein theory, we discuss in detail its embedding into ${\cal N}=8, 6, 4, 2$ supergravity, its spectrum of quadratic fluctuations in all these environments, and the resulting quantum corrections. We find that the $c$-anomaly vanishes only when ${\cal N}\geq 6$, in contrast to the BPS branch where $c$ vanishes for all ${\cal N}\geq 2$. We briefly discuss potential repercussions this feature could have in a microscopic description of these black holes.

hep-th↗

arXiv2017

Tweaking one-loop determinants in AdS$_3$

We revisit the subject of one-loop determinants in AdS$_3$ gravity via the quasinormal mode method. Our goal is to evaluate a one-loop determinant with chiral boundary conditions for the metric field; chirality is achieved by imposing Dirichlet boundary conditions on certain components while others satisfy Neumann. Along the way, we give a generalization of the quasinormal mode method for stationary (non-static) thermal backgrounds, and propose a treatment for Neumann boundary conditions in this framework. We evaluate the graviton one-loop determinant on the Euclidean BTZ background with parity-violating boundary conditions (CSS), and find excellent agreement with the dual warped CFT. We also discuss a more general falloff in AdS$_3$ that is related to two dimensional quantum gravity in lightcone gauge. The behavior of the ghost fields under both sets of boundary conditions is novel and we discuss potential interpretations.

hep-th↗

arXiv2017

Siegel Modular Forms and Black Hole Entropy

We discuss the application of Siegel Modular Forms to Black Hole entropy counting. The role of the Igusa cusp form $χ_{10}$ in the D1D5P system is well-known, and its transformation properties are what allows precision microstate counting in this case. We apply a similar method to extract the Fourier coefficients of other Siegel modular and paramodular forms, and we show that they could serve as candidates for other types of black holes. We investigate the growth of their coefficients, identifying the dominant contributions and the leading logarithmic corrections in various regimes. We also discuss similarities and differences to the behavior of $χ_{10}$, and possible physical interpretations of such forms both from a microscopic and gravitational point of view.

hep-th↗

arXiv2017

The Spectrum of Static Subtracted Geometries

Subtracted geometries are black hole solutions of the four dimensional STU model with rather interesting ties to asymptotically flat black holes. A peculiar feature is that the solutions to the Klein-Gordon equation on this subtracted background can be organized according to representations of the conformal group $SO(2,2)$. We test if this behavior persists for the linearized fluctuations of gravitational and matter fields on static, electrically charged backgrounds of this kind. We find that there is a subsector of the modes that do display conformal symmetry, while some modes do not. We also discuss two different effective actions that describe these subtracted geometries and how the spectrum of quasinormal modes is dramatically different depending upon the action used.

hep-th↗

arXiv2017

Geodesic Diagrams, Gravitational Interactions & OPE Structures

We give a systematic procedure to evaluate conformal partial waves involving symmetric tensors for an arbitrary CFT$_d$ using geodesic Witten diagrams in AdS$_{d+1}$. Using this procedure we discuss how to draw a line between the tensor structures in the CFT and cubic interactions in AdS. We contrast this map to known results using three-point Witten diagrams: the maps obtained via volume versus geodesic integrals differ. Despite these differences, we show how to decompose four-point exchange Witten diagrams in terms of geodesic diagrams, and we discuss the product expansion of local bulk fields in AdS.

hep-th↗

arXiv2017

Entanglement Entropy in Warped Conformal Field Theories

We present a detailed discussion of entanglement entropy in (1+1)-dimensional Warped Conformal Field Theories (WCFTs). We implement the Rindler method to evaluate entanglement and Renyi entropies for a single interval and along the way we interpret our results in terms of twist field correlation functions. Holographically a WCFT can be described in terms of Lower Spin Gravity, a SL(2,R)xU(1) Chern-Simons theory in three dimensions. We show how to obtain the universal field theory results for entanglement in a WCFT via holography. For the geometrical description of the theory we introduce the concept of geodesic and massive point particles in the warped geometry associated to Lower Spin Gravity. In the Chern-Simons description we evaluate the appropriate Wilson line that captures the dynamics of a massive particle.

hep-th↗