POINT-SPLITTING REGULARIZATION IN (SUPER)CONFORMAL FIELD THEORY

1999 ◽  
Vol 14 (18) ◽  
pp. 2887-2904
Author(s):  
BELAL E. BAAQUIE ◽  
KOK KEAN YIM
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Splitting Method ◽  
Central Extensions ◽  
Singular Terms ◽  
Superconformal Field Theory ◽  
Conformal Field ◽  
Point Splitting ◽  
Super Conformal Field Theory ◽  
Wick’S Theorem

The method of point-splitting regularization is applied on the two-dimensional (super)conformal field theory. This method is first used to regularize the fermionic conformal field theory and then the N=1 superconformal field theory. We obtain the correct central extensions for the conformal algebra and the N=1 superconformal algebra. We arrived at these results only after some nontrivial, but exact, cancelations among all the singular terms, as required by the consistency of the point-splitting method. In the course of our analysis, we rederive Wick's Theorem directly from the commutation equations of the fundamental fields.

POINT-SPLITTING REGULARIZATION IN N=2 SUPERCONFORMAL FIELD THEORY

1999 ◽  
Vol 14 (20) ◽  
pp. 3207-3237
Author(s):  
BELAL E. BAAQUIE ◽  
KOK KEAN YIM
Keyword(s):  
Field Theory ◽  
Complex Structure ◽  
Splitting Method ◽  
Superconformal Algebra ◽  
Operator Product ◽  
Central Extensions ◽  
Superconformal Field Theory ◽  
Conformal Field ◽  
Coset Model ◽  
Point Splitting

In this paper, the method of point-splitting regularization is applied on the N=2 superconformal field theory, specifically the superconformal coset model formulated by Kazama and Suzuki. We obtain the correct central extensions for the N=2 superconformal algebra after many nontrivial cancellations among the various singular expressions. This shows the consistency of the point-splitting method in an N=2 superconformal system. In the process, we arrive at the Kazama–Suzuki conditions which govern the existence of an N=2 superconformal coset model in the N=1 coset model. In addition, we obtain a number of mathematical relations between the structure constants and the complex structure of the model, which allow us to simplify the U(1) current of the N=2 superconformal algebra. In the course of our analysis, we found that, at least in a two dimension conformal field theory, the operator product expansion of a composite current must be written in a way which conveys all the information of the commutator equations.

scholarly journals HEISENBERG AND MODULAR INVARIANCE OF N=2 CONFORMAL FIELD THEORY

2000 ◽  
Vol 15 (19) ◽  
pp. 3065-3094
Author(s):  
SHI-SHYR ROAN
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Theta Function ◽  
Central Charge ◽  
Jacobi Form ◽  
Modular Invariance ◽  
Function Representation ◽  
Superconformal Field Theory ◽  
Conformal Field ◽  
Modular Transformations

We present a theta function representation of the twisted characters for the rational N=2 superconformal field theory, and discuss the Jacobi-form like functional properties of these characters for a fixed central charge under the action of a finite Heisenberg group and modular transformations.

FINE STRUCTURE OF THE MVW CORRESPONDENCE

1992 ◽  
Vol 07 (11) ◽  
pp. 2371-2415 ◽  
Author(s):  
TOSHIYA KAWAI
Keyword(s):  
Field Theory ◽  
Quantum Mechanics ◽  
Fine Structure ◽  
Conformal Field Theory ◽  
Singularity Theory ◽  
Conformal Field ◽  
Super Conformal Field Theory

A correspondence observed by Martinec, Vafa and Warner (MVW) between the singularity theory and the N = 2 super conformal field theory is reviewed by using N = 2 SUSY quantum mechanics.

scholarly journals Structure of the Extended Schrödinger–Virasoro Lie Algebra $\widetilde{\mathfrak{sv}}$

2009 ◽  
Vol 16 (04) ◽  
pp. 549-566 ◽  
Author(s):  
Shoulan Gao ◽  
Cuipo Jiang ◽  
Yufeng Pei
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Statistical Physics ◽  
Two Dimensional ◽  
Universal Central Extension ◽  
Central Extensions ◽  
Infinite Dimensional ◽  
Conformal Field

We study the derivations, the central extensions and the automorphism group of the extended Schrödinger–Virasoro Lie algebra [Formula: see text], introduced by Unterberger in the context of two-dimensional conformal field theory and statistical physics. Moreover, we show that [Formula: see text] is an infinite-dimensional complete Lie algebra, and the universal central extension of [Formula: see text] in the category of Leibniz algebras is the same as that in the category of Lie algebras.

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