scholarly journals Fermionic Basis in Conformal Field Theory and Thermodynamic Bethe Ansatz for Excited States

2011 ◽  
Author(s):  
Hermann Boos
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Bethe Ansatz ◽  
Excited States ◽  
Thermodynamic Bethe Ansatz ◽  
Conformal Field

scholarly journals Symmetry-resolved entanglement for excited states and two entangling intervals in AdS3/CFT2

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Konstantin Weisenberger ◽  
Suting Zhao ◽  
Christian Northe ◽  
René Meyer
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Excited States ◽  
Vertex Operator Algebra ◽  
Central Charge ◽  
Entanglement Entropy ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Chern Simons ◽  
Twist Fields

Abstract We test the proposal of [1] for the holographic computation of the charged moments and the resulting symmetry-resolved entanglement entropy in different excited states, as well as for two entangling intervals. Our holographic computations are performed in U(1) Chern-Simons-Einstein-Hilbert gravity, and are confirmed by independent results in a conformal field theory at large central charge. In particular, we consider two classes of excited states, corresponding to charged and uncharged conical defects in AdS3. In the conformal field theory, these states are generated by the insertion of charged and uncharged heavy operators. We employ the monodromy method to calculate the ensuing four-point function between the heavy operators and the twist fields. For the two-interval case, we derive our results on the AdS and the conformal field theory side, respectively, from the generating function method of [1], as well as the vertex operator algebra. In all cases considered, we find equipartition of entanglement between the different charge sectors. We also clarify an aspect of conformal field theories with a large central charge and $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody symmetry used in our calculations, namely the factorization of the Hilbert space into a gravitational Virasoro sector with large central charge, and a $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody sector.

scholarly journals Integrable structure of BCD conformal field theory and boundary Bethe ansatz for affine Yangian

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Alexey Litvinov ◽  
Ilya Vilkoviskiy
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Bethe Ansatz ◽  
Spin Chains ◽  
Unified Approach ◽  
Three Solutions ◽  
Integrable Structure ◽  
Conformal Field

Abstract In these notes we study integrable structures of conformal field theory with BCD symmetry. We realise these integrable structures as $$ \mathfrak{gl} $$ gl (1) affine Yangian “spin chains” with boundaries. We provide three solutions of Sklyanin KRKR equation compatible with the affine Yangian R-matrix and derive Bethe ansatz equations for the spectrum. Our analysis provides a unified approach to the integrable structures with BCD symmetry including superalgebras.

scholarly journals MASSIVE-CONFORMAL DICTIONARY

1994 ◽  
Vol 09 (32) ◽  
pp. 5753-5767 ◽  
Author(s):  
EZER MELZER
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Bethe Ansatz ◽  
Finite Volume ◽  
Energy Levels ◽  
Infinite Volume ◽  
Minimal Models ◽  
Combinatorial Interpretation ◽  
Conformal Field ◽  
Quantum Numbers

The finite-volume spectrum of an integrable massive perturbation of a rational conformal field theory interpolates between massive multiparticle states in infinite-volume (IR limit) and conformal states, which are approached at zero volume (UV limit). Each state is labeled in the IR by a set of “Bethe-ansatz quantum numbers,” while in the UV limit it is characterized primarily by the conformal dimensions of the conformal field creating it. We present explicit conjectures for the UV conformal dimensions corresponding to any IR state in the ϕ1, 3-perturbed minimal models ℳ(2, 5) and ℳ(3, 5). The conjectures, which are based on a combinatorial interpretation of the Rogers-Ramanujan-Schur identities, are consistent with numerical results obtained previously for low-lying energy levels.

scholarly journals SPECTRA IN CONFORMAL FIELD THEORIES FROM THE ROGERS DILOGARITHM

1992 ◽  
Vol 07 (37) ◽  
pp. 3487-3494 ◽  
Author(s):  
A. KUNIBA ◽  
T. NAKANISHI
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Bethe Ansatz ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Universal Form ◽  
Conformal Field ◽  
Functional Relations ◽  
Sum Formula ◽  
Dilogarithm Function

We propose a system of functional relations having a universal form connected to the [Formula: see text] Bethe ansatz equation. Based on the analysis of it, we conjecture a new sum formula for the Rogers dilogarithm function in terms of the scaling dimensions of the [Formula: see text] parafermion conformal field theory.

scholarly journals Symmetry resolved relative entropies and distances in conformal field theory

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Luca Capizzi ◽  
Pasquale Calabrese
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Excited States ◽  
Total System ◽  
Conformal Field ◽  
Analytic Expressions ◽  
Remarkable Result ◽  
Single Interval ◽  
Reduced Density ◽  
Twist Fields

Abstract We develop a systematic approach to compute the subsystem trace distances and relative entropies for subsystem reduced density matrices associated to excited states in different symmetry sectors of a 1+1 dimensional conformal field theory having an internal U(1) symmetry. We provide analytic expressions for the charged moments corresponding to the resolution of both relative entropies and distances for general integer n. For the relative entropies, these formulas are manageable and the analytic continuation to n = 1 can be worked out in most of the cases. Conversely, for the distances the corresponding charged moments become soon untreatable as n increases. A remarkable result is that relative entropies and distances are the same for all symmetry sectors, i.e. they satisfy entanglement equipartition, like the entropies. Moreover, we exploit the OPE expansion of composite twist fields, to provide very general results when the subsystem is a single interval much smaller than the total system. We focus on the massless compact boson and our results are tested against exact numerical calculations in the XX spin chain.

A Review of Conformal Field Theory in 2D

2014 ◽  
Vol 6 (2) ◽  
pp. 1079-1105
Author(s):  
Rahul Nigam
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Conformal Field Theory ◽  
Statistical Mechanics ◽  
Critical Behavior ◽  
Verma Module ◽  
Virasoro Algebra ◽  
Quantum Field ◽  
Conformal Field ◽  
Insight Into

In this review we study the elementary structure of Conformal Field Theory in which is a recipe for further studies of critical behavior of various systems in statistical mechanics and quantum field theory. We briefly review CFT in dimensions which plays a prominent role for example in the well-known duality AdS/CFT in string theory where the CFT lives on the AdS boundary. We also describe the mapping of the theory from the cylinder to a complex plane which will help us gain an insight into the process of radial quantization and radial ordering. Finally we will develop the representation of the Virasoro algebra which is the well-known "Verma module".  

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