scholarly journals STRESS ENERGY TENSOR IN LCFT AND LOGARITHMIC SUGAWARA CONSTRUCTION

2003 ◽  
Vol 18 (25) ◽  
pp. 4771-4788 ◽  
Author(s):  
IAN I. KOGAN ◽  
ALEXANDER NICHOLS
Keyword(s):  
Central Charge ◽  
Energy Tensor ◽  
Conformal Field Theories ◽  
Stress Energy Tensor ◽  
Moody Algebra ◽  
Conformal Field ◽  
Stress Energy ◽  
Dimension One ◽  
Independent Parameters ◽  
Construction Works

We discuss the partners of the stress energy tensor and their structure in Logarithmic conformal field theories. In particular we draw attention to the fundamental differences between theories with zero and non-zero central charge. However they are both characterised by at least two independent parameters. We show how, by using a generalised Sugawara construction, one can calculate the logarithmic partner of T. We show that such a construction works in the c=-2 theory using the conformal dimension one primary currents which generate a logarithmic extension of the Kac-Moody algebra. This is an expanded version of a talk presented by A. Nichols at the conference on Logarithmic Conformal Field Theory and its Applications in Tehran Iran, 2001.

scholarly journals QUANTUM ENERGY INEQUALITIES IN TWO-DIMENSIONAL CONFORMAL FIELD THEORY

2005 ◽  
Vol 17 (05) ◽  
pp. 577-612 ◽  
Author(s):  
CHRISTOPHER J. FEWSTER ◽  
STEFAN HOLLANDS
Keyword(s):  
Field Theories ◽  
Positive Energy ◽  
Energy Tensor ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Stress Energy Tensor ◽  
Quantum Energy ◽  
Conformal Field ◽  
Quantum Energy Inequalities ◽  
Stress Energy

Quantum energy inequalities (QEIs) are state-independent lower bounds on weighted averages of the stress-energy tensor, and have been established for several free quantum field models. We present rigorous QEI bounds for a class of interacting quantum fields, namely the unitary, positive energy conformal field theories (with stress-energy tensor) on two-dimensional Minkowski space. The QEI bound depends on the weight used to average the stress-energy tensor and the central charge(s) of the theory, but not on the quantum state. We give bounds for various situations: averaging along timelike, null and spacelike curves, as well as over a space-time volume. In addition, we consider boundary conformal field theories and more general "moving mirror" models. Our results hold for all theories obeying a minimal set of axioms which — as we show — are satisfied by all models built from unitary highest-weight representations of the Virasoro algebra. In particular, this includes all (unitary, positive energy) minimal models and rational conformal field theories. Our discussion of this issue collects together (and, in places, corrects) various results from the literature which do not appear to have been assembled in this form elsewhere.

EFFECTIVE ACTION FOR QUANTUM GRAVITY IN TWO DIMENSIONS

1989 ◽  
Vol 04 (01) ◽  
pp. 71-81 ◽  
Author(s):  
K. YOSHIDA
Keyword(s):  
Effective Action ◽  
Central Charge ◽  
Two Dimensions ◽  
Energy Tensor ◽  
Moody Algebra ◽  
Generating Functional ◽  
Induced Gravity ◽  
Light Cone Gauge ◽  
Conformal Field ◽  
Stress Energy

The generating functional of the correlation functions of the stress energy tensor in conformal field theory is derived and shown to be equal to the effective action for 2-dimensional induced gravity in the light cone gauge recently given by Polyakov. Seeking the condition for consistent quantization for such an action, one arrives at a chiral SU (2) × SU (2) current algebra. The corresponding Kac-Moody algebra has the central charge given by k = (C − 26)/6.

EFFECTIVE ACTION FOR INDUCED GRAVITY ON A 2-DIMENSIONAL MANIFOLD

1990 ◽  
Vol 05 (23) ◽  
pp. 4559-4578 ◽  
Author(s):  
K. YOSHIDA
Keyword(s):  
Euclidean Plane ◽  
Energy Tensor ◽  
Dimensional Manifold ◽  
Fundamental Change ◽  
Stress Energy Tensor ◽  
Generating Functional ◽  
Induced Gravity ◽  
Conformal Field ◽  
First Case ◽  
Stress Energy

The generating functional of the correlation functions of the stress energy-tensor in conformal field theory is explicitly constructed first on the Euclidean plane and then on an arbitrary Riemann surface. For the first case, one finds “anti-holomorphic” SL(2C) symmetry as the counterpart of the SL(2C) current algebra of Polyakov’s quantized gravity in 2 dimensions. For a general real 2-dimensional manifold, one expects a fundamental change due to the breaking of SL(2C) symmetry and to loss of locality.

scholarly journals Chaos and pole skipping in CFT2

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
David M. Ramirez
Keyword(s):  
Energy Density ◽  
Quantum Chaos ◽  
Central Charge ◽  
Finite Size ◽  
Complex Frequency ◽  
Conformal Field Theories ◽  
Point Function ◽  
Light Spectrum ◽  
Conformal Field ◽  
Stress Energy

Abstract Recent work has suggested an intriguing relation between quantum chaos and energy density correlations, known as pole skipping. We investigate this relationship in two dimensional conformal field theories on a finite size spatial circle by studying the thermal energy density retarded two-point function on a torus. We find that the location ω* = iλ of pole skipping in the complex frequency plane is determined by the central charge and the stress energy one-point function 〈T〉 on the torus. In addition, we find a bound on λ in c > 1 compact, unitary CFT2s identical to the chaos bound, λ ≤ 2πT. This bound is saturated in large c CFT2s with a sparse light spectrum, as quantified by [1], for all temperatures above the dual Hawking-Page transition temperature.

scholarly journals N = 2 SUPERCONFORMAL FIELD THEORY ON THE BASIS OF osp(2|2)

1998 ◽  
Vol 13 (01) ◽  
pp. 47-57 ◽  
Author(s):  
A. SHAFIEKHANI ◽  
W.-S. CHUNG
Keyword(s):  
Central Charge ◽  
Free Field ◽  
Irreducible Representations ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Field Representation ◽  
Superconformal Field Theory ◽  
Systematic Scheme ◽  
Free Field Realization ◽  
Stress Energy

Using a unified and systematic scheme, the free field realization of irreducible representations of osp(2|2) is constructed. By using these realizations, the correlation functions of N = 2 superconformal model based on osp(2|2) symmetry and free field representation of [Formula: see text] generators are calculated. Free field representation of currents are used to determine the stress-energy tensor and the central charge of the model.

NON-STANDARD BOSONIZATION TECHNIQUES IN CONFORMAL FIELD THEORY

1989 ◽  
Vol 04 (05) ◽  
pp. 437-443 ◽  
Author(s):  
ELIAS B. KIRITSIS
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Vertex Operators ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Conformal Field ◽  
Stress Energy

It is shown that G/H models can be constructed in terms of a number of free bosons with a stress energy tensor that contains vertex operators. Generalizations of this technique are also discussed.

scholarly journals Bootstrapping mixed correlators in three-dimensional cubic theories II

2020 ◽  
Vol 8 (6) ◽  
Author(s):  
Stefanos R. Kousvos ◽  
Andreas Stergiou
Keyword(s):  
Condensed Matter ◽  
Three Dimensional ◽  
Global Symmetry ◽  
Energy Tensor ◽  
Conformal Field Theories ◽  
Cubic Symmetry ◽  
Conformal Field ◽  
Conformal Bootstrap ◽  
Perturbative Methods ◽  
Stress Energy

Conformal field theories (CFTs) with cubic global symmetry in 3D are relevant in a variety of condensed matter systems and have been studied extensively with the use of perturbative methods like the \varepsilonε expansion. In an earlier work, we used the nonperturbative numerical conformal bootstrap to provide evidence for the existence of a previously unknown 3D CFT with cubic symmetry, dubbed “Platonic CFT”. In this work, we make further use of the numerical conformal bootstrap to perform a three-dimensional scan in the space of scaling dimensions of three low-lying operators. We find a three-dimensional isolated allowed region in parameter space, which includes both the 3D (decoupled) Ising model and the Platonic CFT. The essential assumptions on the spectrum of operators used to provide the isolated allowed region include the existence of a stress-energy tensor and the irrelevance of certain operators (in the renormalization group sense).

scholarly journals FREE SUPERFIELD REALIZATION OF N=2 QUANTUM SUPER-W3 ALGEBRA

1994 ◽  
Vol 09 (03) ◽  
pp. 271-278 ◽  
Author(s):  
CHANGHYUN AHN
Keyword(s):  
Virasoro Algebra ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Stress Energy ◽  
Dimension One

We rewrite N=2 quantum super-W3 algebra, a nonlinear extended N=2 super Virasoro algebra, containing one additional primary superfield of dimension two which has no U(1) charge, besides the super stress energy tensor of dimension one in N=2 superspace. The free superfield realization of this algebra is obtained by two N=2 chiral fermionic superfields of dimension 1/2 satisfying N=2 complex U(1) Kac-Moody algebras.

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