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.

3D SINGLETONS AND THEIR BOUNDARY 2D CONFORMAL FIELD THEORY

1999 ◽  
Vol 11 (09) ◽  
pp. 1079-1090 ◽  
Author(s):  
SÉBASTIEN MICHÉA
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Recent Work ◽  
De Sitter Space ◽  
Field Theories ◽  
Conformal Field Theories ◽  
De Sitter ◽  
Witt Algebra ◽  
Conformal Field ◽  
De Sitter Universe

This paper is a continuation of recent work of Flato and Frønsdal on singletons in 1+2 anti De Sitter universe and their link with 2D conformal field theories on the boundary. More specifically we show that in this framework we can construct a 3D-singleton model in the bulk, the limit of which on the boundary of De Sitter space is a Gupta–Bleuler triplet for two commuting copies of the Witt algebra. We also generalize this result to the case of WZNW models.

RESHETIKHIN-TURAEV AND CRANE-KOHNO-KONTSEVICH 3-MANIFOLD INVARIANTS COINCIDE

1993 ◽  
Vol 02 (01) ◽  
pp. 65-95 ◽  
Author(s):  
SERGEY PIUNIKHIN
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Explicit Formula ◽  
Quantum Groups ◽  
Jones Polynomial ◽  
Matrix Elements ◽  
Conformal Blocks ◽  
Conformal Field ◽  
Wznw Model ◽  
The Matrix

The coincidence of two different presentations of Witten 3-manifold invariants is proved. One of them, invented by Reshetikhin and Turaev, is based on the surgery presentation a of 3-manifold and the representation theory of quantum groups; another one, invented by Kohno and Crane and, in slightly different language by Kontsevich, is based on a Heegaard decomposition of a 3-manifold and representations of the Teichmuller group, arising in conformal field theory. The explicit formula for the matrix elements of generators of the Teichmuller group in the space of conformal blocks in the SU(2) k, WZNW-model is given,using the Jones polynomial of certain links.

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".  

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