DIFFERENTIAL EQUATIONS IN g≥2 CONFORMAL FIELD THEORY

1989 ◽  
Vol 04 (18) ◽  
pp. 1773-1782
Author(s):  
AKISHI KATO ◽  
TOMOKI NAKANISHI
Keyword(s):  
Differential Equations ◽  
Riemann Surfaces ◽  
Virasoro Algebra ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Highest Weight ◽  
Higher Genus ◽  
Highest Weight Representations ◽  
Null State

We consider the minimal conformal field theories on Riemann surfaces of genus greater than one. We illustrate in a simple example how the null state conditions in the highest weight representations of the Virasoro algebra turn into differential equations including the moduli variables for correlators between degenerate fields. In particular, the set of an infinite number of partial differential equations satisfied by higher genus characters is obtained.

scholarly journals OPERATOR PRODUCT EXPANSION IN SL(2) CONFORMAL FIELD THEORY

2002 ◽  
Vol 17 (11) ◽  
pp. 683-693 ◽  
Author(s):  
KAZUO HOSOMICHI ◽  
YUJI SATOH
Keyword(s):  
Field Theory ◽  
Operator Product Expansion ◽  
Field Theories ◽  
Operator Product ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Highest Weight ◽  
Wznw Model ◽  
Highest Weight Representations ◽  
Highest Weight Representation

In the conformal field theories having affine SL(2) symmetry, we study the operator product expansion (OPE) involving primary fields in highest weight representations. For this purpose, we analyze properties of primary fields with definite SL(2) weights, and calculate their two- and three-point functions. Using these correlators, we show that the correct OPE is obtained when one of the primary fields belongs to the degenerate highest weight representation. We briefly comment on the OPE in the SL (2,R) WZNW model.

scholarly journals PURELY AFFINE ELEMENTARY su(N) FUSIONS

2002 ◽  
Vol 17 (19) ◽  
pp. 1249-1258 ◽  
Author(s):  
JØRGEN RASMUSSEN ◽  
MARK A. WALTON
Keyword(s):  
Linear Combination ◽  
Lie Algebras ◽  
Tensor Products ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Simple Lie Algebras ◽  
Conformal Field ◽  
Highest Weight ◽  
Highest Weight Representations

We consider three-point couplings in simple Lie algebras — singlets in triple tensor products of their integrable highest weight representations. A coupling can be expressed as a linear combination of products of finitely many elementary couplings. This carries over to affine fusion, the fusion of Wess–Zumino–Witten conformal field theories, where the expressions are in terms of elementary fusions. In the case of su(4) it has been observed that there is a purely affine elementary fusion, i.e. an elementary fusion that is not an elementary coupling. In this paper we show by construction that there is at least one purely affine elementary fusion associated to every su (N > 3).

scholarly journals Dipolar quantization and the infinite circumference limit of two-dimensional conformal field theories

2016 ◽  
Vol 31 (32) ◽  
pp. 1650170 ◽  
Author(s):  
Nobuyuki Ishibashi ◽  
Tsukasa Tada
Keyword(s):  
Virasoro Algebra ◽  
Field Theories ◽  
Inner Product ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Vacuum States ◽  
Quantum Statistical ◽  
Statistical Systems ◽  
Continuous Index

Elaborating on our previous presentation, where the term dipolar quantization was introduced, we argue here that adopting [Formula: see text] as the Hamiltonian instead of [Formula: see text] yields an infinite circumference limit in two-dimensional conformal field theory. The new Hamiltonian leads to dipolar quantization instead of radial quantization. As a result, the new theory exhibits a continuous and strongly degenerated spectrum in addition to the Virasoro algebra with a continuous index. Its Hilbert space exhibits a different inner product than that obtained in the original theory. The idiosyncrasy of this particular Hamiltonian is its relation to the so-called sine-square deformation, which is found in the study of a certain class of quantum statistical systems. The appearance of the infinite circumference explains why the vacuum states of sine-square deformed systems are coincident with those of the respective closed-boundary systems.

Higher genus partition functions of meromorphic conformal field theories

2009 ◽  
Vol 2009 (06) ◽  
pp. 048-048 ◽  
Author(s):  
Matthias R Gaberdiel ◽  
Roberto Volpato
Keyword(s):  
Field Theories ◽  
Partition Functions ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Higher Genus
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