Conformal field theory, real weight differentials and KdV equation in higher genus

1990 ◽  
pp. 163-175
Author(s):  
Marco Matone
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Kdv Equation ◽  
Conformal Field ◽  
Higher Genus

scholarly journals SU(2)k×SU(2)l/SU(2)k+l COSET CONFORMAL FIELD THEORY AND TOPOLOGICAL MINIMAL MODEL ON HIGHER GENUS RIEMANN SURFACE

1993 ◽  
Vol 08 (31) ◽  
pp. 5537-5561 ◽  
Author(s):  
HITOSHI KONNO
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Riemann Surface ◽  
Vertex Operator ◽  
Correlation Functions ◽  
Minimal Model ◽  
The Other ◽  
Operator Formalism ◽  
Conformal Field ◽  
Higher Genus

We consider the Feigin-Fuchs-Felder formalism of the SU (2)k× SU (2)l/ SU (2)k+l coset minimal conformal field theory and extend it to higher genus. We investigate a double BRST complex with respect to two compatible BRST charges, one associated with the parafermion sector and the other associated with the minimal sector in the theory. The usual screened vertex operator is extended to the BRST-invariant screened three-string vertex. We carry out a sewing operation of these vertices and derive the BRST-invariant screened g-loop operator. The latter operator characterizes the higher genus structure of the theory. An analogous operator formalism for the topological minimal model is obtained as the limit l=0 of the coset theory. We give some calculations of correlation functions on higher genus.

CORRELATORS OF CONFORMAL FIELD THEORIES FROM THEIR CHARACTERS

1990 ◽  
Vol 05 (31) ◽  
pp. 2643-2649
Author(s):  
R. P. MALIK ◽  
N. BEHERA ◽  
R. K. KAUL
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Riemann Surface ◽  
Complete Solution ◽  
Arbitrary Point ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Higher Genus

All genus characters define a complete solution of a two-dimensional rational conformal field theory. An arbitrary point correlator can be obtained by an appropriate combination of the pinchings of zero-homology and non-zero-homology cycles of the characters on the higher genus Riemann surface.

scholarly journals A guide to two-dimensional conformal field theory

2019 ◽  
pp. 60-120
Author(s):  
Jörg Teschner
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Virasoro Algebra ◽  
Integrable Models ◽  
Two Dimensional ◽  
Isomonodromic Deformation ◽  
Conformal Field ◽  
Deformation Problem ◽  
Basic Formalism ◽  
Higher Genus

This is a review of two-dimensional conformal field theory including the Virasoro algebra, the bootstrap, and some of the relations to integrable models. An effort is made to develop the basic formalism in a way which is both elementary but also as flexible as possible at the same time. Some advanced topics such as conformal field theory on higher genus surfaces and relations to the isomonodromic deformation problem are discussed; for other topics we offer a first guide to the literature.

scholarly journals Real weight b-c systems and conformal field theory in higher genus

1990 ◽  
Vol 334 (3) ◽  
pp. 717-744 ◽  
Author(s):  
Loriano Bonora ◽  
Marco Matone ◽  
Francesco Toppan ◽  
Ke Wu
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Conformal Field ◽  
Higher Genus

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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