Chapter 6. Lax integrable systems and conformal field theory

2012 ◽  
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Integrable Systems ◽  
Conformal Field

scholarly journals Controlled Loewner-Kufarev Equation Embedded into the Universal Grassmannian

2020 ◽  
Author(s):  
Takafumi Amaba ◽  
◽  
Roland Friedrich ◽  
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Explicit Formula ◽  
Integrable Systems ◽  
Witt Algebra ◽  
Tau Function ◽  
Driving Function ◽  
Conformal Field

We introduce the class of controlled Loewner-Kufarev equations and consider aspects of their algebraic nature. We lift the solution of such a controlled equation to the (Sato)-Segal-Wilson Grassmannian, and discuss its relation with the tau-function. We briefly highlight relations of the Grunsky matrix with integrable systems and conformal field theory. Our main result is the explicit formula which expresses the solution of the controlled equation in terms of the signature of the driving function through the action of words in generators of the Witt algebra.

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
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