scholarly journals The Regge limit of AdS3 holographic correlators with heavy states: towards the black hole regime

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Nejc Čeplak ◽  
Marcel R. R. Hughes
Keyword(s):  
Black Hole ◽  
Phase Shift ◽  
Central Charge ◽  
Bulk Phase ◽  
Conformal Dimension ◽  
Order Relations ◽  
Conical Defect ◽  
Point Correlation ◽  
Light Probe ◽  
Regge Limit

Abstract We examine the Regge limit of holographic 4-point correlation functions in AdS3× S3 involving two heavy and two light operators. In this kinematic regime such correlators can be reconstructed from the bulk phase shift accumulated by the light probe as it traverses the geometry dual to the heavy operator. We work perturbatively — but to arbitrary orders — in the ratio of the heavy operator’s conformal dimension to the dual CFT2’s central charge, thus going beyond the low order results of [1] and [2]. In doing so, we derive all-order relations between the bulk phase shift and the Regge limit OPE data of a class of heavy-light multi-trace operators exchanged in the cross-channel. Furthermore, we analyse two examples for which the relevant 4-point correlators are known explicitly to all orders: firstly the case of heavy operators dual to AdS3 conical defect geometries and secondly the case of non-trivial smooth geometries representing microstates of the two-charge D1-D5 black hole.

scholarly journals The Regge limit of AdS3 holographic correlators

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Stefano Giusto ◽  
Marcel R.R. Hughes ◽  
Rodolfo Russo
Keyword(s):  
Central Charge ◽  
Minimal Solution ◽  
Tree Level ◽  
Leading Order ◽  
Conformal Dimension ◽  
Anomalous Dimensions ◽  
Conical Defect ◽  
Pure States ◽  
Regge Limit

Abstract We study the Regge limit of 4-point AdS3× S3 correlators in the tree-level supergravity approximation and provide various explicit checks of the relation between the eikonal phase derived in the bulk picture and the anomalous dimensions of certain double-trace operators. We consider both correlators involving all light operators and HHLL correlators with two light and two heavy multi-particle states. These heavy operators have a conformal dimension proportional to the central charge and are pure states of the theory, dual to asymptotically AdS3× S3 regular geometries. Deviation from AdS3× S3 is parametrised by a scale μ and is related to the conformal dimension of the dual heavy operator. In the HHLL case, we work at leading order in μ and derive the CFT data relevant to the bootstrap relations in the Regge limit. Specifically, we show that the minimal solution to these equations relevant for the conical defect geometries is different to the solution implied by the microstate geometries dual to pure states.

scholarly journals Black holes, heavy states, phase shift and anomalous dimensions

2019 ◽  
Vol 6 (6) ◽  
Author(s):  
Manuela Kulaxizi ◽  
Gim Seng Ng ◽  
Andrei Parnachev
Keyword(s):  
Black Hole ◽  
Phase Shift ◽  
Central Charge ◽  
Complete Agreement ◽  
Black Hole Mass ◽  
Point Function ◽  
Expansion Parameter ◽  
Anomalous Dimensions ◽  
Leading Term ◽  
Regge Limit

We compute the phase shift of a highly energetic particle traveling in the background of an asymptotically AdS black hole. In the dual CFT, the phase shift is related to a four point function in the Regge limit. The black hole mass is translated to the ratio between the conformal dimension of a heavy operator and the central charge. This ratio serves as a useful expansion parameter; its power measures the number of stress tensors appearing in the intermediate channel. We compute the leading term in the phase shift in a holographic CFT of arbitrary dimensionality using Conformal Regge Theory and observe complete agreement with the gravity result. In a two-dimensional CFT with a large central charge the heavy-heavy-light-light Virasoro vacuum block reproduces the gravity phase shift to all orders in the expansion parameter. We show that the leading order phase shift is related to the anomalous dimensions of certain double trace operators and verify this agreement using known results for the latter. We also perform a separate gravity calculation of these anomalous dimensions to second order in the expansion parameter and compare with the phase shift expansion.

scholarly journals Holographic thermal correlators revisited

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Hare Krishna ◽  
D. Rodriguez-Gomez
Keyword(s):  
Black Hole ◽  
Leading Order ◽  
Point Function ◽  
Position Space ◽  
Conformal Dimension ◽  
General Contraction ◽  
Neutral Operator ◽  
Point Correlation ◽  
Leading Term ◽  
Geodesic Approximation

Abstract We study 2-point correlation functions for scalar operators in position space through holography including bulk cubic couplings as well as higher curvature couplings to the square of the Weyl tensor. We focus on scalar operators with large conformal dimensions. This allows us to use the geodesic approximation for propagators. In addition to the leading order contribution, captured by geodesics anchored at the insertion points of the operators on the boundary and probing the bulk geometry thoroughly studied in the literature, the first correction is given by a Witten diagram involving both the bulk cubic coupling and the higher curvature couplings. As a result, this correction is proportional to the VEV of a neutral operator Ok and thus probes the interior of the black hole exactly as in the case studied by Grinberg and Maldacena [13]. The form of the correction matches the general expectations in CFT and allows to identify the contributions of TnOk (being Tn the general contraction of n energy-momentum tensors) to the 2-point function. This correction is actually the leading term for off-diagonal correlators (i.e. correlators for operators of different conformal dimension), which can then be computed holographically in this way.

scholarly journals Bulk phase shift, CFT Regge limit and Einstein gravity

2018 ◽  
Vol 2018 (6) ◽  
Author(s):  
Manuela Kulaxizi ◽  
Andrei Parnachev ◽  
Alexander Zhiboedov
Keyword(s):  
Phase Shift ◽  
Einstein Gravity ◽  
Bulk Phase ◽  
Regge Limit

scholarly journals Analytic conformal bootstrap and Virasoro primary fields in the Ashkin-Teller model

2021 ◽  
Vol 11 (5) ◽  
Author(s):  
Nikita Nemkov ◽  
Sylvain Ribault
Keyword(s):  
Correlation Functions ◽  
Central Charge ◽  
Theta Functions ◽  
Conformal Dimension ◽  
Conformal Blocks ◽  
Conformal Bootstrap ◽  
Crossing Symmetry ◽  
Point Correlation ◽  
Structure Constants ◽  
Twist Fields

We revisit the critical two-dimensional Ashkin–Teller model, i.e. the \mathbb{Z}_2ℤ2 orbifold of the compactified free boson CFT at c=1c=1. We solve the model on the plane by computing its three-point structure constants and proving crossing symmetry of four-point correlation functions. We do this not only for affine primary fields, but also for Virasoro primary fields, i.e. higher twist fields and degenerate fields. This leads us to clarify the analytic properties of Virasoro conformal blocks and fusion kernels at c=1c=1. We show that blocks with a degenerate channel field should be computed by taking limits in the central charge, rather than in the conformal dimension. In particular, Al. Zamolodchikov’s simple explicit expression for the blocks that appear in four-twist correlation functions is only valid in the non-degenerate case: degenerate blocks, starting with the identity block, are more complicated generalized theta functions.

scholarly journals ENTROPY OF THE THREE-DIMENSIONAL SCHWARZSCHILD–de SITTER BLACK HOLE

2001 ◽  
Vol 16 (36) ◽  
pp. 2353-2357 ◽  
Author(s):  
Y. S. MYUNG
Keyword(s):  
Black Hole ◽  
Central Charge ◽  
Three Dimensional ◽  
De Sitter Space ◽  
De Sitter ◽  
Correct Definition ◽  
Conical Defect ◽  
Entropy Bounds ◽  
Definition Of ◽  
Cardy Formula

We study the three-dimensional Schwarzschild–de Sitter ( SdS 3) black hole which corresponds essentially to a conical defect. We compute the mass of the SdS 3 black hole from the correct definition of the mass in asymptotically de Sitter space. Then we clarify the relation between the mass, entropy and temperature for this black hole without any ambiguity. We also establish the SdS 3/ CFT 2-correspondence for the entropy by applying the Cardy formula to a CFT with a central charge c = 3ℓ/2G3. Finally we discuss the entropy bounds for the SdS 3 black hole.

scholarly journals Correlation functions in finite temperature CFT and black hole singularities

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
D. Rodriguez-Gomez ◽  
J.G. Russo
Keyword(s):  
Black Hole ◽  
Event Horizon ◽  
Correlation Functions ◽  
Finite Temperature ◽  
Proper Time ◽  
Black Brane ◽  
Point Function ◽  
Black Hole Singularity ◽  
Point Correlation ◽  
Scaling Dimension

Abstract We compute thermal 2-point correlation functions in the black brane AdS5 background dual to 4d CFT’s at finite temperature for operators of large scaling dimension. We find a formula that matches the expected structure of the OPE. It exhibits an exponentiation property, whose origin we explain. We also compute the first correction to the two-point function due to graviton emission, which encodes the proper time from the event horizon to the black hole singularity.

scholarly journals Central charges for AdS black holes

2021 ◽  
Author(s):  
Malcolm Perry ◽  
Maria J Rodriguez
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Cosmological Constant ◽  
Central Charge ◽  
Negative Cosmological Constant ◽  
Ads Black Holes ◽  
Kerr Black Holes ◽  
Distinguishing Features ◽  
Area Law ◽  
Cardy Formula

Abstract Nontrivial diffeomorphisms act on the horizon of a generic 4D black holes and create distinguishing features referred to as soft hair. Amongst these are a left-right pair of Virasoro algebras with associated charges that reproduce the Bekenstein-Hawking entropy for Kerr black holes. In this paper we show that if one adds a negative cosmological constant, there is a similar set of infinitesimal diffeomorphisms that act non-trivially on the horizon. The algebra of these diffeomorphisms gives rise to a central charge. Adding a boundary counterterm, justified to achieve integrability, leads to well-defined central charges with cL = cR. The macroscopic area law for Kerr-AdS black holes follows from the assumption of a Cardy formula governing the black hole microstates.

scholarly journals Fix the dual geometries of $$T\bar{T}$$ deformed CFT$$_2$$ and highly excited states of CFT$$_2$$

2020 ◽  
Vol 80 (12) ◽  
Author(s):  
Peng Wang ◽  
Houwen Wu ◽  
Haitang Yang
Keyword(s):  
Black Hole ◽  
Excited States ◽  
Conformal Symmetry ◽  
Propagation Speed ◽  
Conformally Flat ◽  
Btz Black Hole ◽  
Perfect Agreement ◽  
Conical Defect ◽  
Dual Geometries ◽  
Btz Metric

AbstractIn previous works, we have developed an approach to fix the leading behaviors of the pure AdS$$_3$$ 3 and BTZ black hole from the entanglement entropies of the free CFT$$_2$$ 2 and finite temperature CFT$$_2$$ 2 , respectively. We exclusively use holographic principle only and make no restriction about the bulk geometry, not only the kinematics but also the dynamics. In order to verify the universality and correctness of our method, in this paper, we apply it to the $$T\bar{T}$$ T T ¯ deformed CFT$$_2$$ 2 , which breaks the conformal symmetry. In terms of the physical arguments of the $$T\bar{T}$$ T T ¯ deformed CFT$$_2$$ 2 , the derived metric is a deformed BTZ black hole. The requirement that the CFT$$_2$$ 2 lives on a conformally flat boundary leads to $$r_{c}^{2}=\ 6R_{AdS}^{4}/(\pi c\mu )$$ r c 2 = 6 R AdS 4 / ( π c μ ) naturally, in perfect agreement with previous conjectures in literature. The energy spectum and propagation speed calculated with this deformed BTZ metric are the same as these derived from $$T\bar{T}$$ T T ¯ deformed CFT$$_2$$ 2 . We furthermore fix the dual geometry of highly excited states with our approach. The result contains the descriptions for the conical defect and BTZ black hole.

scholarly journals A NEAR HORIZON CFT DUAL FOR KERR–NEWMAN AdS

2011 ◽  
Vol 26 (18) ◽  
pp. 3077-3090 ◽  
Author(s):  
BRADLY K. BUTTON ◽  
LEO RODRIGUEZ ◽  
CATHERINE A. WHITING ◽  
TUNA YILDIRIM
Keyword(s):  
Black Hole ◽  
Energy Momentum Tensor ◽  
Central Charge ◽  
Virasoro Algebra ◽  
Momentum Tensor ◽  
Two Dimensional ◽  
S Wave ◽  
One Dimensional ◽  
Conformal Field ◽  
Asymptotic Symmetries

We show that the near horizon regime of a Kerr–Newman AdS (KNAdS) black hole, given by its two-dimensional analogue a là Robinson and Wilczek (Phys. Rev. Lett.95, 011303 (2005)), is asymptotically AdS2 and dual to a one-dimensional quantum conformal field theory (CFT). The s-wave contribution of the resulting CFT's energy–momentum tensor together with the asymptotic symmetries, generate a centrally extended Virasoro algebra, whose central charge reproduces the Bekenstein–Hawking entropy via Cardy's formula. Our derived central charge also agrees with the near extremal Kerr/CFT correspondence (Phys. Rev. D80, 124008 (2009)) in the appropriate limits. We also compute the Hawking temperature of the KNAdS black hole by coupling its Robinson and Wilczek two-dimensional analogue (RW2DA) to conformal matter.

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