EXACT SOLUTIONS OF CONFORMAL FIELD THEORY IN TWO DIMENSIONS AND CRITICAL PHENOMENA

1989 ◽  
Vol 01 (02n03) ◽  
pp. 197-234 ◽  
Author(s):  
A. B. ZAMOLODCHIKOV
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Critical Phenomena ◽  
Virasoro Algebra ◽  
Two Dimensions ◽  
Minimal Models ◽  
Infinite Dimensional ◽  
Superconformal Field Theory ◽  
Conformal Field ◽  
Modern Development

Modern development of conformal field theory in two dimensions and its applications to critical phenomena are briefly reviewed. The specific properties of the renormalization group in two dimensions and the fundamentals of 2-dimensional conformal field theory are presented. The properties of degenerate representations of the Virasoro algebra and other infinite dimensional algebras, "minimal" models of conformal and superconformal field theory, "parafermionic" and other symmetries are discussed. We also investigate a perturbation theory around conformal solutions of field theory.

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".  

scholarly journals Parafermionization, bosonization, and critical parafermionic theories

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Yuan Yao ◽  
Akira Furusaki
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Degrees Of Freedom ◽  
Lattice Models ◽  
Partition Functions ◽  
Minimal Models ◽  
Fermionic Model ◽  
Conformal Field ◽  
Critical Theories ◽  
Wigner Transformation

AbstractWe formulate a ℤk-parafermionization/bosonization scheme for one-dimensional lattice models and field theories on a torus, starting from a generalized Jordan-Wigner transformation on a lattice, which extends the Majorana-Ising duality atk= 2. The ℤk-parafermionization enables us to investigate the critical theories of parafermionic chains whose fundamental degrees of freedom are parafermionic, and we find that their criticality cannot be described by any existing conformal field theory. The modular transformations of these parafermionic low-energy critical theories as general consistency conditions are found to be unconventional in that their partition functions on a torus transform differently from any conformal field theory whenk >2. Explicit forms of partition functions are obtained by the developed parafermionization for a large class of critical ℤk-parafermionic chains, whose operator contents are intrinsically distinct from any bosonic or fermionic model in terms of conformal spins and statistics. We also use the parafermionization to exhaust all the ℤk-parafermionic minimal models, complementing earlier works on fermionic cases.

scholarly journals HEISENBERG AND MODULAR INVARIANCE OF N=2 CONFORMAL FIELD THEORY

2000 ◽  
Vol 15 (19) ◽  
pp. 3065-3094
Author(s):  
SHI-SHYR ROAN
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Theta Function ◽  
Central Charge ◽  
Jacobi Form ◽  
Modular Invariance ◽  
Function Representation ◽  
Superconformal Field Theory ◽  
Conformal Field ◽  
Modular Transformations

We present a theta function representation of the twisted characters for the rational N=2 superconformal field theory, and discuss the Jacobi-form like functional properties of these characters for a fixed central charge under the action of a finite Heisenberg group and modular transformations.

scholarly journals KERR–BOLT SPACETIMES AND KERR/CFT CORRESPONDENCE

2012 ◽  
Vol 27 (08) ◽  
pp. 1250046 ◽  
Author(s):  
A. M. GHEZELBASH
Keyword(s):  
Field Theory ◽  
Boundary Condition ◽  
Black Hole ◽  
Conformal Field Theory ◽  
Virasoro Algebra ◽  
Conformal Field ◽  
Higher Dimensional ◽  
Dimensional Black Hole ◽  
Horizon Geometry ◽  
Cardy Formula

We study the extremal rotating spacetimes with a NUT twist in the context of recently proposed Kerr/CFT correspondence. The Kerr/CFT correspondence states that the near-horizon states of an extremal four (or higher) dimensional black hole could be identified with a certain chiral conformal field theory. The corresponding Virasoro algebra is generated with a class of diffeomorphism which preserves an appropriate boundary condition on the near-horizon geometry. We combine the calculated central charges with the expected form of the temperature, using the Cardy formula to obtain the microscopically entropy of the extremal rotating spacetimes with a NUT twist. All results are in agreement with the macroscopic entropy of the extremal spacetimes.

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