MODULAR INVARIANCE FOR THE N=2 TWISTED SUPERCONFORMAL ALGEBRA

1988 ◽  
Vol 03 (02) ◽  
pp. 127-137 ◽  
Author(s):  
V.K. Dobrev ◽  
A. Ch. Ganchev
Keyword(s):  
Central Charge ◽  
Superconformal Algebra ◽  
Field Theories ◽  
Modular Invariance ◽  
Two Dimensional ◽  
Invariance Properties ◽  
Highest Weight ◽  
Modular Transformations ◽  
Highest Weight Representations

We study the modular invariance properties of two-dimensional N=2 twisted superconformal invariant field theories. We express the characters of the unitarizable highest weight representations with central charge c=1−2/m, m=2, 3,..., in terms of certain θ—functions with characteristics. We give the modular transformations of the characters and obtain the modular invariance structures. The structures differ in the cases m=0 mod 4 and m=2 mod 4, while the cases of m odd are subcases of 4m. The latter is illustrated for m=3.

scholarly journals On 2d CFTs that interpolate between minimal models

2019 ◽  
Vol 6 (6) ◽  
Author(s):  
Sylvain Ribault
Keyword(s):  
Correlation Functions ◽  
Central Charge ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Conformal Blocks ◽  
Conformal Field ◽  
Exactly Solvable ◽  
Structure Constants

We investigate exactly solvable two-dimensional conformal field theories that exist at generic values of the central charge, and that interpolate between A-series or D-series minimal models. When the central charge becomes rational, correlation functions of these CFTs may tend to correlation functions of minimal models, or diverge, or have finite limits which can be logarithmic. These results are based on analytic relations between four-point structure constants and residues of conformal blocks.

SUPERCONFORMAL ORBIFOLDS INVOLVING THE FERMION NUMBER OPERATOR

2004 ◽  
Vol 19 (22) ◽  
pp. 3637-3667 ◽  
Author(s):  
KATRIN WENDLAND
Keyword(s):  
Central Charge ◽  
Space Time ◽  
Field Theories ◽  
Two Dimensional ◽  
Number Operator ◽  
Superconformal Field Theories ◽  
Fermion Number ◽  
Multicritical Points ◽  
Arbitrary Dimensions ◽  
Charge Formula

We consider orbifolds of two-dimensional unitary toroidal superconformal field theories with target spaces of arbitrary dimensions, where the orbifold group involves the space–time fermion number operator. We construct all so-called superaffine, orbifold prime and super-M-orbifold models by generalizing the constructions of Dixon, Ginsparg and Harvey. We also correct claims made by Dixon, Ginsparg and Harvey about multicritical points among those models with central charge [Formula: see text].

AN EXPLICIT FORMULA FOR SOME SINGULAR VECTORS OF THE NEVEU–SCHWARZ ALGEBRA

1992 ◽  
Vol 07 (13) ◽  
pp. 3023-3033 ◽  
Author(s):  
LOUIS BENOIT ◽  
YVAN SAINT-AUBIN
Keyword(s):  
Explicit Expression ◽  
Explicit Formula ◽  
Singular Vector ◽  
Central Charge ◽  
Discrete Series ◽  
Virasoro Algebra ◽  
Verma Modules ◽  
Singular Vectors ◽  
Highest Weight ◽  
Highest Weight Representations

Similarly to the Virasoro algebra, the Neveu–Schwarz algebra has a discrete series of unitary irreducible highest weight representations. These are labeled by the values of [Formula: see text] (the central charge) and of the highest weight hpq = [(p (m + 2) − qm)2 − 4]/(8m (m + 2)) where m, p, q are some integers. The Verma modules constructed with these values (c, h) are not irreducible, however, as they contain two Verma submodules, each generated by a singular vector ψp,q (of weight hpq + pq/2) and ψm−p, m+2−q (of weight hpq + (m−p)(m+2−q)/2), respectively. We give an explicit expression for these singular vectors whenever one of its indices is 1.

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 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.

scholarly journals UNITARY REPRESENTATIONS OF W INFINITY ALGEBRAS

1992 ◽  
Vol 07 (25) ◽  
pp. 6339-6355 ◽  
Author(s):  
SATORU ODAKE
Keyword(s):  
Central Charge ◽  
Discrete Series ◽  
Free Field ◽  
Unitary Representations ◽  
Continuous Series ◽  
Highest Weight ◽  
Free Field Realization ◽  
Highest Weight Representations

We study the irreducible unitary highest weight representations, which are obtained from free field realizations, of W infinity algebras [Formula: see text] with central charges (2, 1, 3, 2M, N, 2M+N). The characters of these representations are computed. We construct a new extended superalgebra [Formula: see text], whose bosonic sector is [Formula: see text]. Its representations obtained from a free field realization with central charge 2M+N, are classified into two classes: continuous series and discrete series. For the former there exists a supersymmetry, but for the latter a supersymmetry exists only for M=N.

scholarly journals Analysis for Lorentzian conformal field theories through sine-square deformation

2020 ◽  
Vol 2020 (6) ◽  
Author(s):  
Xun Liu ◽  
Tsukasa Tada
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Continuous Spectrum ◽  
Central Charge ◽  
Virasoro Algebra ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
The Third

Abstract We reexamine two-dimensional Lorentzian conformal field theory using the formalism previously developed in a study of sine-square deformation of Euclidean conformal field theory. We construct three types of Virasoro algebra. One of them reproduces the result by Lüscher and Mack, while another type exhibits divergence in the central charge term. The third leads to a continuous spectrum and contains no closed time-like curve in the system.

IMPROVED FORMULATION OF GNO FERMIONIZATION THEOREM

1989 ◽  
Vol 04 (11) ◽  
pp. 1013-1025 ◽  
Author(s):  
P. FRE’ ◽  
F. GLIOZZI ◽  
A. PIRAS
Keyword(s):  
Partition Function ◽  
Symmetric Space ◽  
Modular Group ◽  
Central Charge ◽  
Free Fermion ◽  
Moody Algebra ◽  
Modular Invariant ◽  
Regular Embedding ◽  
Highest Weight ◽  
Highest Weight Representations

It is pointed out that in the Kac-Moody algebras fulfilling the fermionization criterion of Goddard, Nahm and Olive and having a non-minimal value of the central charge k, only a proper subset of the allowed unitary highest weight representations can actually be encoded in a free fermion theory. These truly fermionizable representations are selected by a very specific non-regular embedding of the fermionizable Kac-Moody algebra into the lowest level SO (N F ) Kac-Moody algebra, N F being both the number of fermions and the dimension of the GNO symmetric space. This embedding is a particular case of the embeddings considered by Bais and Bouwknegt and by Schellekens and Warner, for which the Virasoro central charge of the subgroup is equal to that of the group. Furthermore, these fermionizable representations span an orbit of the modular group always leading to a non trivial modular invariant partition function.

Sign in / Sign up

Export Citation Format

Share Document