We compute one-loop corrections to the euclidean gravitational path integral of near-extremal (anti-)de Sitter-Kerr black hole in terms of the connection coefficients of the Heun equation describing the black hole linear perturbations in the Teukolsky formalism. We show that different near-extremal limits lead to distinct physical properties of the gravitational configuration, as they get described by distinct limiting differential equations. As a result, the light modes emerging in the limit determine different scaling properties in the temperature of the one-loop determinants. We show that the cold case displays distinctive universal log(T) corrections to the entropy of the system, including the ultracold regime. On the contrary, these do not appear in the limit in which the event horizon superimposes onto the cosmological one. In the Schwarzschild-de Sitter case, a further check is performed by comparison with the Denef-Hartnoll-Sachdev formula.

United Kingdom

Paolo Arnaudo

Italy

Giulio Bonelli

Alessandro Tanzini

One loop corrections to the thermodynamics of near-extremal Kerr-(A)dS black holes from Heun equation

<p>We propose a method to perform an exact calculation of one-loop quantum corrections to black hole entropy in terms of Virasoro semiclassical blocks. We analyze in detail a four-dimensional Kerr black hole and show that in the near-extremal limit a branch of long-lived modes arises. We prove that the contribution of these modes accounts for a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mi>s</mi><mo>−</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo stretchy="false">)</mo><mi>log</mi><msub><mrow><mi>T</mi></mrow><mrow><mtext>Hawking</mtext></mrow></msub></mrow></math> correction to the entropy for massless particles of spin <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi><mo>=</mo><mn>1</mn></math>, 2. We show that in the full calculation performed in the exact Kerr background the leading contribution actually is sourced by the near-horizon region only, and as such has a universal validity for any asymptotic behavior at infinity.</p>

One-Loop Corrections to Near-Extremal Kerr Thermodynamics from Semiclassical Virasoro Blocks

We compute new exact analytic expressions for one-loop scalar effective actions in Kerr (A)dS black hole (BH) backgrounds in four and five dimensions. These are computed by the connection coefficients of the Heun equation via a generalization of the Gelfand-Yaglom formalism to second-order linear ordinary differential equations with regular singularities. The expressions we find are in terms of Nekrasov-Shatashvili special functions, making explicit the analytic properties of the one-loop effective actions with respect to the gravitational parameters and the precise contributions of the quasinormal modes. The latter arise via an associated integrable system. In particular, we prove asymptotic formulas for large angular momenta in terms of hypergeometric functions and give a precise mathematical meaning to Rindler-like region contributions. Moreover, we identify the leading terms in the large distance expansion as the point particle approximation of the BH and their finite size corrections as encoding the BH tidal response. We also discuss the exact properties of the thermal version of the BH effective actions by providing a proof of the Denef-Hartnoll-Sachdev formula and explicitly computing it for new relevant cases. Although we focus on the real scalar field in dS-Kerr and (A)dS-Schwarzschild in four and five dimensions, similar formulas can be given for higher spin matter and radiation fields in more general gravitational backgrounds.

One loop effective actions in Kerr-(A)dS black holes

We present a novel study of Kerr Compton amplitudes in a partial wave basis in terms of the Nekrasov-Shatashvili (NS) function of the confluent Heun equation (CHE). Remarkably, NS-functions enjoy analytic properties and symmetries that are naturally inherited by the Compton amplitudes. Based on this, we characterize the analytic dependence of the Compton phase shift in the Kerr spin parameter and provide a direct comparison to the standard post-Minkowskian (PM) perturbative approach within general relativity (GR). We also analyze the universal large frequency behavior of the relevant characteristic exponent of the CHE—also known as the renormalized angular momentum—and find agreement with numerical computations. Moreover, we discuss the analytic continuation in the harmonics quantum number <math><mo>ℓ</mo></math> of the partial wave, and show that the limit to the physical integer values commutes with the PM expansion of the observables. Finally, we obtain the contributions to the tree-level, point-particle, gravitational Compton amplitude in a covariant basis through <math><mi>O</mi><mo>(</mo><msubsup><mi>a</mi><mi>BH</mi><mn>8</mn></msubsup><mo>)</mo></math>, without the need to take the superextremal limit for Kerr spin.

France

Yilber Fabian Bautista

Switzerland

Cristoforo Iossa

United States

Zihan Zhou

Black hole perturbation theory meets <math><mrow><msub><mrow><mi>CFT</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math>: Kerr-Compton amplitudes from Nekrasov-Shatashvili functions

We study black hole linear perturbation theory in a four-dimensional Schwarzschild (anti) de Sitter background. When dealing with a positive cosmological constant, the corresponding spectral problem is solved systematically via the Nekrasov-Shatashvili functions or, equivalently, classical Virasoro conformal blocks. However, this approach can be more complicated to implement for certain perturbations if the cosmological constant is negative. For these cases, we propose an alternative method to set up perturbation theory for both small and large black holes in an analytical manner. Our analysis reveals a new underlying recursive structure that involves multiple polylogarithms. We focus on gravitational, electromagnetic, and conformally coupled scalar perturbations subject to Dirichlet and Robin boundary conditions. The low-lying modes of the scalar sector of gravitational perturbations and its hydrodynamic limit are studied in detail.

Gleb Aminov

CERN

Alba Grassi

Black hole perturbation theory and multiple polylogarithms

We give explicit expressions for the finite frequency greybody factor, quasinormal modes, and Love numbers of Kerr black holes by computing the exact connection coefficients of the radial and angular parts of the Teukolsky equation. This is obtained by solving the connection problem of the confluent Heun equation in terms of the explicit expression of irregular Virasoro conformal blocks as sums over partitions via the Alday, Gaiotto, and Tachikawa correspondence. In the relevant approximation limits our results are in agreement with existing literature. The method we use can be extended to solve the linearized Einstein equation in other interesting gravitational backgrounds.

Daniel Panea Lichtig

Exact solution of Kerr black hole perturbations via <math><mrow><msub><mrow><mi>CFT</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math> and instanton counting: Greybody factor, quasinormal modes, and Love numbers

We show that the nonperturbative dynamics of <math><mi>N</mi><mo>=</mo><mn>2</mn></math> super-Yang-Mills theories in a self-dual <math><mi>Ω</mi></math> background and with arbitrary simple gauge group is fully determined by studying renormalization group equations of vacuum expectation values of surface operators generating one-form symmetries. The corresponding system of equations is a nonautonomous Toda chain, the time being the renormalization group scale. We obtain new recurrence relations which provide a systematic algorithm computing multi-instanton corrections from the tree-level one-loop prepotential as the asymptotic boundary condition of the renormalization group equations. We exemplify by computing the <math><msub><mi>E</mi><mn>6</mn></msub></math> and <math><msub><mi>G</mi><mn>2</mn></msub></math> cases up to two instantons.

Fran Globlek

Counting Yang-Mills Instantons by Surface Operator Renormalization Group Flow

We compute the elliptic genus of the D1/D7 brane system in flat space, finding a non-trivial dependence on the number of D7 branes, and provide an F-theory interpretation of the result. We show that the JK-residues contributing to the elliptic genus are in one-to-one correspondence with coloured plane partitions and that the elliptic genus can be written as a chiral correlator of vertex operators on the torus. We also study the quantum mechanical system describing D0/D6 bound states on a circle, which leads to a plethystic exponential formula that can be connected to the M-theory graviton index on a multi-Taub-NUT background. The formula is a conjectural expression for higher-rank equivariant K-theoretic Donaldson-Thomas invariants on ℂ 3.

Francesco Benini

Matteo Poggi

Elliptic non-Abelian Donaldson-Thomas invariants of ℂ 3

We compute the exact path integral of   <math> <mi>N</mi> <mspace width="0.25em"></mspace> <mo>=</mo> <mn>2</mn> </math>  $$ \mathcal{N} = 2 $$  supersymmetric gauge theories with general gauge group on ℝℙ4 and a ℤ2-quotient of the hemi-S 4. By specializing to SU(2) superconformal quivers, we show that these, together with hemi-S 4 partition functions, compute Liouville correlators on unoriented/open Riemann surfaces. We perform explicit checks for Riemann surfaces obtained as ℤ2 quotients of the sphere and the torus. We also discuss the coupled 3d−4d systems associated to Liouville amplitudes with boundary punctures.

India

Aditya Bawane

Sergio Benvenuti

Nouman Muteeb

<math> <mi>N</mi> <mspace width="0.25em"></mspace> <mo>=</mo> <mn>2</mn> </math>  $$ \mathcal{N} = 2 $$  gauge theories on unoriented/open four-manifolds and their AGT counterparts

We consider the problem of exact integration of the  <math><mi>T</mi><mover><mi>T</mi><mo>¯</mo></mover></math> $$ T\overline{T} $$ -deformation of two dimensional quantum field theories, as well as some higher dimensional extensions in the form of det T -deformations. When the action can be shown to only depend algebraically on the background metric the solution of the deformation equation on the Lagrangian can be given in closed form in terms of solutions of the (extended) Burgers’ equation. We present such examples in two and higher dimensions.