scholarly journals On conformal field theory and stochastic Loewner evolution

2004 ◽  
Vol 687 (3) ◽  
pp. 279-302 ◽  
Author(s):  
R. Friedrich ◽  
J. Kalkkinen
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Stochastic Loewner Evolution ◽  
Conformal Field ◽  
Loewner Evolution

CONFORMAL FIELD THEORY IN TWO DIMENSIONS

2006 ◽  
Vol 21 (11) ◽  
pp. 2237-2258
Author(s):  
JASBIR NAGI
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Operator Algebra ◽  
Two Dimensions ◽  
Stochastic Loewner Evolution ◽  
Conformal Field ◽  
Logarithmic Conformal Field Theory ◽  
Loewner Evolution ◽  
Mathematical Problems ◽  
The Subject

Conformal field theory in two dimensions has, over the years, been an extremely useful tool for a variety of physical and mathematical problems. In this paper, perhaps one of the most profound and foundational aspects of the subject is reviewed in detail, namely that of an operator algebra of the theory. This aspect is then demonstrated in some modern applications, first stochastic Loewner evolution and then logarithmic conformal field theory.

scholarly journals Asymptotic Analysis of Dotsenko–Fateev Integrals

2019 ◽  
Vol 20 (11) ◽  
pp. 3799-3848 ◽  
Author(s):  
Jonatan Lenells ◽  
Fredrik Viklund
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Asymptotic Analysis ◽  
Conformal Field ◽  
Contour Integrals ◽  
Loewner Evolution

Abstract We develop a method for evaluating asymptotics of certain contour integrals that appear in conformal field theory under the name of Dotsenko–Fateev integrals and that are natural generalizations of the classical hypergeometric functions.We illustrate the method by establishing a number of estimates that are useful in the context of martingale observables for multiple Schramm–Loewner evolution processes.

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 THE FREE FIELD REPRESENTATION OF SU(3) CONFORMAL FIELD THEORY

1993 ◽  
Vol 08 (23) ◽  
pp. 4031-4053
Author(s):  
HOVIK D. TOOMASSIAN
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Correlation Functions ◽  
Free Field ◽  
Field Representation ◽  
Conformal Field ◽  
Point Correlation

The structure of the free field representation and some four-point correlation functions of the SU(3) conformal field theory are considered.

scholarly journals Decoherence in Conformal Field Theory

2020 ◽  
Vol 2020 (2) ◽  
Author(s):  
Adolfo del Campo ◽  
Tadashi Takayanagi
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Conformal Field

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.

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