scholarly journals THREE-POINT FUNCTIONS IN CONFORMAL FIELD THEORY WITH AFFINE LIE GROUP SYMMETRY

1999 ◽  
Vol 14 (08) ◽  
pp. 1225-1259 ◽  
Author(s):  
JØRGEN RASMUSSEN
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Lie Group ◽  
General Procedure ◽  
Group Symmetry ◽  
Conformal Field ◽  
Highest Weight ◽  
Integer Solutions ◽  
Lie Group Symmetry ◽  
General Method

In this paper we develop a general method for constructing three-point functions in conformal field theory with affine Lie group symmetry, continuing our recent work on two-point functions. The results are provided in terms of triangular coordinates used in a wave function description of vectors in highest weight modules. In this framework, complicated couplings translate into ordinary products of certain elementary polynomials. The discussions pertain to all simple Lie groups and arbitrary integrable representation. An interesting by-product is a general procedure for computing tensor product coefficients, essentially by counting integer solutions to certain inequalities. As an illustration of the construction, we consider in great detail the three cases SL(3), SL(4) and SO(5).

scholarly journals The Batalin–Vilkovisky Algebra in the String Topology of Classifying Spaces

2019 ◽  
Vol 71 (4) ◽  
pp. 843-889
Author(s):  
Katsuhiko Kuribayashi ◽  
Luc Menichi
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Lie Group ◽  
Hochschild Cohomology ◽  
General Theorem ◽  
String Topology ◽  
Classifying Spaces ◽  
Classifying Space ◽  
Conformal Field ◽  
Connected Lie Group

AbstractFor almost any compact connected Lie group$G$and any field$\mathbb{F}_{p}$, we compute the Batalin–Vilkovisky algebra$H^{\star +\text{dim}\,G}(\text{LBG};\mathbb{F}_{p})$on the loop cohomology of the classifying space introduced by Chataur and the second author. In particular, if$p$is odd or$p=0$, this Batalin–Vilkovisky algebra is isomorphic to the Hochschild cohomology$HH^{\star }(H_{\star }(G),H_{\star }(G))$. Over$\mathbb{F}_{2}$, such an isomorphism of Batalin–Vilkovisky algebras does not hold when$G=\text{SO}(3)$or$G=G_{2}$. Our elaborate considerations on the signs in string topology of the classifying spaces give rise to a general theorem on graded homological conformal field theory.

A comment on quantum group symmetry in conformal field theory

1989 ◽  
Vol 328 (3) ◽  
pp. 557-574 ◽  
Author(s):  
Gregory Moore ◽  
Nicolai Reshetikhin
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Quantum Group ◽  
Group Symmetry ◽  
Conformal Field

scholarly journals Lie group weight multiplicities from conformal field theory

1995 ◽  
Vol 28 (9) ◽  
pp. 2617-2625 ◽  
Author(s):  
T Gannon ◽  
C Jakovljevic ◽  
M A Walton
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Lie Group ◽  
Conformal Field

scholarly journals On the Real Part of a Conformal Field Theory

Universe ◽  
2018 ◽  
Vol 4 (9) ◽  
pp. 97
Author(s):  
Doron Gepner ◽  
Hervé Partouche
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Coulomb Gas ◽  
Field Theories ◽  
Partition Functions ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Conformal Field ◽  
Exceptional Holonomy ◽  
General Method

Every conformal field theory has the symmetry of taking each field to its adjoint. We consider here the quotient (orbifold) conformal field theory obtained by twisting with respect to this symmetry. A general method for computing such quotients is developed using the Coulomb gas representation. Examples of parafermions, S U ( 2 ) current algebra and the N = 2 minimal models are described explicitly. The partition functions and the dimensions of the disordered fields are given. This result is a tool for finding new theories. For instance, it is of importance in analyzing the conformal field theories of exceptional holonomy manifolds.

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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