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".  

QUANTIZING FIELD THEORIES IN NONCOMMUTATIVE GEOMETRY AND THE AdS/CFT CORRESPONDENCE

2000 ◽  
Vol 14 (22n23) ◽  
pp. 2355-2358 ◽  
Author(s):  
KAMRAN KAVIANI
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Conformal Field Theory ◽  
Noncommutative Geometry ◽  
Field Theories ◽  
Quantum Field ◽  
Conformal Field ◽  
Logarithmic Conformal Field Theory

By using the approach of noncommutative geometry, we study spinors and scalars on the two layers AdSd+1 space. We have found that in the boundary of two layers AdSd+1 Space, by using the AdS/CFT correspondence, we have a logarithmic conformal field theory. This observation propose a way to get the quantum field theory in the context of noncommutative geometry.

scholarly journals TQFT VERSUS RCFT: 3-D TOPOLOGICAL INVARIANTS

1995 ◽  
Vol 10 (04) ◽  
pp. 331-336
Author(s):  
BOGUSŁAW BRODA
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Conformal Field Theory ◽  
Three Dimensional ◽  
Topological Quantum Field Theory ◽  
Topological Invariants ◽  
Quantum Field ◽  
Conformal Field ◽  
Topological Quantum

A straightforward relationship between the two approaches to three-dimensional topological invariants, one of them put forward by Witten in the framework of topological quantum field theory, and the second one proposed by Kohno in terms of rational conformal field theory, is established.

scholarly journals GEOMETRIC MODULAR ACTION FOR DISJOINT INTERVALS AND BOUNDARY CONFORMAL FIELD THEORY

2010 ◽  
Vol 22 (03) ◽  
pp. 331-354 ◽  
Author(s):  
ROBERTO LONGO ◽  
PIERRE MARTINETTI ◽  
KARL-HENNING REHREN
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Conformal Field Theory ◽  
Modular Group ◽  
Vacuum State ◽  
Quantum Field ◽  
Conformal Field ◽  
Local Algebras

In suitable states, the modular group of local algebras associated with unions of disjoint intervals in chiral conformal quantum field theory acts geometrically. We translate this result into the setting of boundary conformal QFT and interpret it as a relation between temperature and acceleration. We also discuss novel aspects ("mixing" and "charge splitting") of geometric modular action for unions of disjoint intervals in the vacuum state.

scholarly journals Advances in String Theory in Curved Backgrounds: A Synthesis Report

2003 ◽  
Vol 18 (12) ◽  
pp. 2011-2022 ◽  
Author(s):  
N. G. Sanchez
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
String Theory ◽  
Quantum Field ◽  
De Sitter ◽  
Conformal Field ◽  
Dual Relation ◽  
New Feature ◽  
Synthesis Report ◽  
Gravitational Wave Background

A synthetic report of the advances in the study of classical and quantum string dynamics in curved backgrounds is provided, namely : the new feature of Multistring solutions; the mass spectrum of Strings in Curved backgrounds; The effect of a Cosmological Constant and of Spacial Curvature on Classical and Quantum Strings; Classical splitting of Fundamental Strings; The General String Evolution in constant Curvature Spacetimes; The Conformal Invariance Effects; Strings on plane fronted and gravitational shock waves, string falling on spacetime singularities and its spectrum. New Developments in String Gravity and String Cosmology are reported: String driven cosmology and its Predictions; The primordial gravitational wave background; Non-singular string cosmologies from Exact Conformal Field Theories; Quantum Field Theory, String Temperature and the String Phase of de Sitter space-time; Hawking Radiation in String Theory and the String Phase of Black Holes; New Dual Relation between Quantum Field Theory regime and String regime and the "QFT/String Tango"; New Coherent String States and Minimal Uncertainty Principle in string theory.

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