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 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 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 Disentangling the thermofield-double state

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Pouria Dadras
Keyword(s):  
Field Theory ◽  
Black Hole ◽  
Strong Coupling ◽  
Entanglement Entropy ◽  
Coarse Grained ◽  
One Dimension ◽  
Leading Order ◽  
Point Function ◽  
Replica Trick ◽  
Large N

Abstract In this paper, we consider the evolution of the thermofield-double state under the double-traced operator that connects its both sides. We will compute the entanglement entropy of the resulting state using the replica trick for the large N field theory. To leading order, it can be computed from the two-point function of the theory, where, in CFTs, it is fixed by the symmetries. Due to the exponential decay of the interaction, the entanglement entropy saturates about the thermal time after the interaction is on. Next, we restrict ourselves to one dimension and assume that the theory at strong coupling is effectively described by the Schwarzian action. We then compute the coarse-grained entropy of the resulting state using the four-point function. The equality of the two entropies implies that the double-traced operators in our theory act coherently. In AdS/CFT correspondence where the thermofield-double state corresponds to a two-sided black hole, the action of a double-traced operator corresponds to shrinking or expanding the black hole in the bulk.

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 Loops in AdS: from the spectral representation to position space. Part II

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Dean Carmi
Keyword(s):  
Spectral Representation ◽  
Tree Level ◽  
Point Function ◽  
Position Space ◽  
Gross Neveu Model ◽  
Loop Amplitudes

Abstract We continue the study of AdS loop amplitudes in the spectral representation and in position space. We compute the finite coupling 4-point function in position space for the large-N conformal Gross Neveu model on AdS3. The resummation of loop bubble diagrams gives a result proportional to a tree-level contact diagram. We show that certain families of fermionic Witten diagrams can be easily computed from their companion scalar diagrams. Thus, many of the results and identities of [1] are extended to the case of external fermions. We derive a spectral representation for ladder diagrams in AdS. Finally, we compute various bulk 2-point correlators, extending the results of [1].

scholarly journals BMS modular diaries: torus one-point function

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Arjun Bagchi ◽  
Poulami Nandi ◽  
Amartya Saha ◽  
Zodinmawia
Keyword(s):  
Cosmological Solution ◽  
Three Dimensions ◽  
Field Theories ◽  
Point Function ◽  
Asymptotic Structure ◽  
Highest Weight ◽  
Structure Constants ◽  
Flat Spacetimes ◽  
Geodesic Approximation ◽  
Highest Weight Representation

Abstract Two dimensional field theories invariant under the Bondi-Metzner-Sachs (BMS) group are conjectured to be dual to asymptotically flat spacetimes in three dimensions. In this paper, we continue our investigations of the modular properties of these field theories. In particular, we focus on the BMS torus one-point function. We use two different methods to arrive at expressions for asymptotic structure constants for general states in the theory utilising modular properties of the torus one-point function. We then concentrate on the BMS highest weight representation, and derive a host of new results, the most important of which is the BMS torus block. In a particular limit of large weights, we derive the leading and sub-leading pieces of the BMS torus block, which we then use to rederive an expression for the asymptotic structure constants for BMS primaries. Finally, we perform a bulk computation of a probe scalar in the background of a flatspace cosmological solution based on the geodesic approximation to reproduce our field theoretic results.

scholarly journals TOWARDS THE PROOF OF AGT-W RELATION: TODA 3-POINT FUNCTION AND ${\mathcal W}_{1+\infty}$ ALGEBRA

2013 ◽  
Vol 21 ◽  
pp. 138-139
Author(s):  
SHOTARO SHIBA
Keyword(s):  
Field Theory ◽  
Correlation Function ◽  
Point Function ◽  
Gauge Groups ◽  
Promising Direction ◽  
Quiver Gauge Theory ◽  
Conformal Theory ◽  
Conformal Field ◽  
Point Correlation ◽  
Point Correlation Function

The AGT-W relation is a conjecture of the nontrivial duality between 4-dim quiver gauge theory and 2-dim conformal field theory. We verify a part of this conjecture for all the cases of quiver gauge groups by studying on the property of 3-point correlation function of conformal theory. We also mention the relation to [Formula: see text] algebra as one of the promising direction towards the proof of the remaining part.

scholarly journals Weak Deflection Angle of some Classes of non-linear Electrodynamics Black Holes via Gauss-Bonnet Theorem

2020 ◽  
Author(s):  
Hasan El Moumni ◽  
Karima Masmar ◽  
Ali Övgün
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Gravitational Lensing ◽  
Deflection Angle ◽  
Weak Field ◽  
Leading Order ◽  
Plasma Medium ◽  
Non Linear ◽  
The Deflection Angle ◽  
Bonnet Theorem

In this paper, we study the gravitational lensing by some black hole classes within the non-linear electrodynamics in weak field limits. First, we calculate an optical geometry of the non-linear electrodynamics black hole then we use the Gauss-Bonnet theorem for finding deflection angle in weak field limits. The effect of non-linear electrodynamics on the deflection angle in leading order terms is studied. Furthermore, we discuss the effects of the plasma medium on the weak deflection angle.

scholarly journals Computing three-point correlation function randoms counts without the randoms catalogue

2019 ◽  
Vol 486 (1) ◽  
pp. L105-L109 ◽  
Author(s):  
David W Pearson ◽  
Lado Samushia
Keyword(s):  
Cosmological Parameters ◽  
Synthetic Data ◽  
Function Estimation ◽  
Point Function ◽  
Simple Method ◽  
Galaxy Surveys ◽  
Counting Algorithms ◽  
Data Points ◽  
Point Correlation ◽  
Point Correlation Function

ABSTRACT As we move towards future galaxy surveys, the three-point statistics will be increasingly leveraged to enhance the constraining power of the data on cosmological parameters. An essential part of the three-point function estimation is performing triplet counts of synthetic data points in random catalogues. Since triplet counting algorithms scale at best as $\mathcal {O}(N^2\log N)$ with the number of particles and the random catalogues are typically at least 50 times denser than the data; this tends to be by far the most time-consuming part of the measurements. Here, we present a simple method of computing the necessary triplet counts involving uniform random distributions through simple one-dimensional integrals. The method speeds up the computation of the three-point function by orders of magnitude, eliminating the need for random catalogues, with the simultaneous pair and triplet counting of the data points alone being sufficient.

ONE-LOOP CORRECTION TO ENERGY OF SPINNING STRINGS IN AdS5×T1, 1

2012 ◽  
Vol 27 (03) ◽  
pp. 1250015
Author(s):  
HYOJOONG KIM ◽  
NAKWOO KIM ◽  
JUNG HUN LEE
Keyword(s):  
Field Theory ◽  
Mode Frequency ◽  
Harmonic Oscillators ◽  
Quantum Corrections ◽  
Gauge Field Theory ◽  
Leading Order ◽  
Loop Correction ◽  
Conformal Dimension ◽  
Normal Mode Frequency ◽  
The One

We consider circular spinning string solutions in AdS5×T1, 1 and calculate the quantum corrections to the energy at one-loop on worldsheet. The fluctuations are given as a set of harmonic oscillators and we calculate their normal mode frequency in closed form. The sum of frequency is equal to the one-loop string energy, which through AdS/CFT correspondence corresponds to the leading order correction of the conformal dimension for long operators in Klebanov–Witten conifold gauge field theory.

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