scholarly journals Cutoff AdS3 versus $$ T\overline{T} $$ CFT2 in the large central charge sector: correlators of energy-momentum tensor

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Yi Li ◽  
Yang Zhou
Keyword(s):  
Field Theory ◽  
Euclidean Plane ◽  
Energy Momentum Tensor ◽  
Central Charge ◽  
Momentum Tensor ◽  
Two Dimensional ◽  
Conformal Field ◽  
Operator Identity ◽  
Pure Gravity ◽  
Charge Sector

Abstract In this article we probe the proposed holographic duality between $$ T\overline{T} $$ T T ¯ deformed two dimensional conformal field theory and the gravity theory of AdS3 with a Dirichlet cutoff by computing correlators of energy-momentum tensor. We focus on the large central charge sector of the $$ T\overline{T} $$ T T ¯ CFT in a Euclidean plane and a sphere, and compute the correlators of energy-momentum tensor using an operator identity promoted from the classical trace relation. The result agrees with a computation of classical pure gravity in Euclidean AdS3 with the corresponding cutoff surface, given a holographic dictionary which identifies gravity parameters with $$ T\overline{T} $$ T T ¯ CFT parameters.

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.

scholarly journals SPACETIME NONCOMMUTATIVITY WITH A BIFERMIONIC PARAMETER

2008 ◽  
Vol 23 (12) ◽  
pp. 887-893 ◽  
Author(s):  
D. M. GITMAN ◽  
D. V. VASSILEVICH
Keyword(s):  
Field Theory ◽  
Finite Number ◽  
Energy Momentum Tensor ◽  
Canonical Quantization ◽  
Momentum Tensor ◽  
Theory Model ◽  
Two Dimensional ◽  
Noncommutative Field Theory ◽  
Moyal Product ◽  
Moyal Plane

We consider a Moyal plane and propose to make the noncommutativity parameter Θμν bifermionic, i.e. composed of two fermionic (Grassmann odd) parameters. The Moyal product then contains a finite number of derivatives, which avoid the difficulties of the standard approach. As an example, we construct a two-dimensional noncommutative field theory model based on the Moyal product with a bifermionic parameter and show that it has a locally conserved energy–momentum tensor. The model has no problem with the canonical quantization and appears to be renormalizable.

scholarly journals Scrambling with conservation laws

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Gong Cheng ◽  
Brian Swingle
Keyword(s):  
Field Theory ◽  
Conservation Laws ◽  
Energy Momentum Tensor ◽  
Einstein Gravity ◽  
Momentum Tensor ◽  
Late Time ◽  
Current Operator ◽  
Conformal Field ◽  
Time Value ◽  
The Impact

Abstract In this article we discuss the impact of conservation laws, specifically U(1) charge conservation and energy conservation, on scrambling dynamics, especially on the approach to the late time fully scrambled state. As a model, we consider a d + 1 dimensional (d ≥ 2) holographic conformal field theory with Einstein gravity dual. Using the holographic dictionary, we calculate out-of-time-order-correlators (OTOCs) that involve the conserved U(1) current operator or energy-momentum tensor. We show that these OTOCs approach their late time value as a power law in time, with a universal exponent $$ \frac{d}{2} $$ d 2 . We also generalize the result to compute OTOCs between general operators which have overlap with the conserved charges.

scholarly journals Analysis for Lorentzian conformal field theories through sine-square deformation

2020 ◽  
Vol 2020 (6) ◽  
Author(s):  
Xun Liu ◽  
Tsukasa Tada
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Continuous Spectrum ◽  
Central Charge ◽  
Virasoro Algebra ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
The Third

Abstract We reexamine two-dimensional Lorentzian conformal field theory using the formalism previously developed in a study of sine-square deformation of Euclidean conformal field theory. We construct three types of Virasoro algebra. One of them reproduces the result by Lüscher and Mack, while another type exhibits divergence in the central charge term. The third leads to a continuous spectrum and contains no closed time-like curve in the system.

scholarly journals Conformal field theory complexity from Euler-Arnold equations

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Mario Flory ◽  
Michal P. Heller
Keyword(s):  
Field Theory ◽  
Optimization Problem ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Conformal Field Theories ◽  
Gaussian States ◽  
Conformal Field ◽  
Main Challenge ◽  
Differential Generalization ◽  
Comprehensive Study

Abstract Defining complexity in quantum field theory is a difficult task, and the main challenge concerns going beyond free models and associated Gaussian states and operations. One take on this issue is to consider conformal field theories in 1+1 dimensions and our work is a comprehensive study of state and operator complexity in the universal sector of their energy-momentum tensor. The unifying conceptual ideas are Euler-Arnold equations and their integro-differential generalization, which guarantee well-posedness of the optimization problem between two generic states or transformations of interest. The present work provides an in-depth discussion of the results reported in arXiv:2005.02415 and techniques used in their derivation. Among the most important topics we cover are usage of differential regularization, solution of the integro-differential equation describing Fubini-Study state complexity and probing the underlying geometry.

scholarly journals Symmetry-resolved entanglement in AdS3/CFT2 coupled to U(1) Chern-Simons theory

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Suting Zhao ◽  
Christian Northe ◽  
René Meyer
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Gauge Field ◽  
Wilson Line ◽  
Entanglement Entropy ◽  
Simons Theory ◽  
Two Dimensional ◽  
Conformal Field ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We consider symmetry-resolved entanglement entropy in AdS3/CFT2 coupled to U(1) Chern-Simons theory. We identify the holographic dual of the charged moments in the two-dimensional conformal field theory as a charged Wilson line in the bulk of AdS3, namely the Ryu-Takayanagi geodesic minimally coupled to the U(1) Chern-Simons gauge field. We identify the holonomy around the Wilson line as the Aharonov-Bohm phases which, in the two-dimensional field theory, are generated by charged U(1) vertex operators inserted at the endpoints of the entangling interval. Furthermore, we devise a new method to calculate the symmetry resolved entanglement entropy by relating the generating function for the charged moments to the amount of charge in the entangling subregion. We calculate the subregion charge from the U(1) Chern-Simons gauge field sourced by the bulk Wilson line. We use our method to derive the symmetry-resolved entanglement entropy for Poincaré patch and global AdS3, as well as for the conical defect geometries. In all three cases, the symmetry resolved entanglement entropy is determined by the length of the Ryu-Takayanagi geodesic and the Chern-Simons level k, and fulfills equipartition of entanglement. The asymptotic symmetry algebra of the bulk theory is of $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody type. Employing the $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody symmetry, we confirm our holographic results by a calculation in the dual conformal field theory.

scholarly journals Two point functions in defect CFTs

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Christopher P. Herzog ◽  
Abhay Shrestha
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Correlation Functions ◽  
Equations Of Motion ◽  
Physical Space ◽  
Arbitrary Spin ◽  
Momentum Tensor ◽  
Maxwell Theory ◽  
Conformal Field ◽  
Point Correlation

Abstract This paper is designed to be a practical tool for constructing and investigating two-point correlation functions in defect conformal field theory, directly in physical space, between any two bulk primaries or between a bulk primary and a defect primary, with arbitrary spin. Although geometrically elegant and ultimately a more powerful approach, the embedding space formalism gets rather cumbersome when dealing with mixed symmetry tensors, especially in the projection to physical space. The results in this paper provide an alternative method for studying two-point correlation functions for a generic d-dimensional conformal field theory with a flat p-dimensional defect and d − p = q co-dimensions. We tabulate some examples of correlation functions involving a conserved current, an energy momentum tensor and a Maxwell field strength, while analysing the constraints arising from conservation and the equations of motion. A method for obtaining bulk-to-defect correlators is also explained. Some explicit examples are considered: free scalar theory on ℝp× (ℝq/ℤ2) and a free four dimensional Maxwell theory on a wedge.

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