Structure constants for rational conformal field theories

1988 ◽  
Vol 215 (1) ◽  
pp. 124-128 ◽  
Author(s):  
P. Di Francesco
Keyword(s):  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Structure Constants

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.

scholarly journals DILOGARITHM IDENTITIES, FUSION RULES AND STRUCTURE CONSTANTS OF CFTs

1994 ◽  
Vol 09 (02) ◽  
pp. 133-141 ◽  
Author(s):  
MICHAEL TERHOEVEN
Keyword(s):  
Central Charge ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Fusion Rules ◽  
Conformal Field ◽  
Physics Literature ◽  
Structure Constants ◽  
Quantum Dimensions ◽  
Infinite Set ◽  
Modular Covariance

Recently dilogarithm identities have made their appearance in the physics literature. These identities seem to allow to calculate structure constants like, in particular, the effective central charge of certain conformal field theories from their fusion rules. In Ref. 12 a proof of identities of this type was given by considering the asymptotics of character functions in the so-called Rogers-Ramanujan sum form and comparing with the asymptotics predicted by modular covariance. Refining the argument, we obtain the general connection of quantum dimensions of certain conformal field theories to the arguments of the dilogarithm function in the identities in question and an infinite set of consistency conditions on the parameters of Rogers-Ramanujan type partitions for them to be modular covariant.

scholarly journals Fixed points and D-branes

2013 ◽  
Vol 94 (108) ◽  
pp. 169-180
Author(s):  
Elaine Beltaos
Keyword(s):  
Fixed Point ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Point Property ◽  
Integer Matrix ◽  
Matrix Representations ◽  
Fusion Ring ◽  
Conformal Field ◽  
S Matrix ◽  
Structure Constants

The affine Kac-Moody algebras give rise to rational conformal field theories (RCFTs) called the Wess-Zumino-Witten (WZW) models. An important component of an RCFT is its fusion ring, whose structure constants are given by the associated S-matrix. We apply a fixed point property possessed by the WZW models ("fixed point factorization") to calculate nonnegative integer matrix representations of the fusion ring, allowing for the calculation of D-brane charges in string theory.

THREE-POINT CORRELATION FUNCTIONS OF THE MINIMAL CONFORMAL THEORIES COUPLED TO 2D GRAVITY

1991 ◽  
Vol 06 (39) ◽  
pp. 3601-3612 ◽  
Author(s):  
Vl. S. DOTSENKO
Keyword(s):  
Operator Algebra ◽  
Correlation Functions ◽  
2D Gravity ◽  
Coulomb Gas ◽  
Field Theories ◽  
Algebra Structure ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Point Correlation ◽  
Structure Constants

The general three-point correlation functions of the minimal conformal field theories coupled to gravity are calculated using the specific Coulomb gas type quantization technique. The gravity interaction modifies in an essential way the operator algebra of the corresponding minimal model, in particular in canceling the decoupling of a finite number of primary fields, in case of rational theories. This is suggested to be related to the appearance of new physical states, under the BRST analysis of Lian and Zuckerman. Within the analytic technique, this effect is due to the corresponding singularities of the gravity sector operator algebra structure constants.

scholarly journals Defects and perturbation

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Enrico M. Brehm
Keyword(s):  
Entanglement Entropy ◽  
Topological Defects ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Conformal Field

Abstract We investigate perturbatively tractable deformations of topological defects in two-dimensional conformal field theories. We perturbatively compute the change in the g-factor, the reflectivity, and the entanglement entropy of the conformal defect at the end of these short RG flows. We also give instances of such flows in the diagonal Virasoro and Super-Virasoro Minimal Models.

scholarly journals Entanglement and complexity of purification in ( 1+1 )-dimensional free conformal field theories

2021 ◽  
Vol 3 (1) ◽  
Author(s):  
Hugo A. Camargo ◽  
Lucas Hackl ◽  
Michal P. Heller ◽  
Alexander Jahn ◽  
Tadashi Takayanagi ◽  
...  
Keyword(s):  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field

scholarly journals NON-ABELIAN FRACTIONAL QUANTUM HALL STATES AND CHIRAL COSET CONFORMAL FIELD THEORIES

2000 ◽  
Vol 15 (30) ◽  
pp. 4857-4870 ◽  
Author(s):  
D. C. CABRA ◽  
E. FRADKIN ◽  
G. L. ROSSINI ◽  
F. A. SCHAPOSNIK
Keyword(s):  
Quantum Hall ◽  
Field Theories ◽  
Simons Theory ◽  
Conformal Field Theories ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Conformal Field ◽  
Quantum Hall States ◽  
Effective Lagrangian ◽  
Chern Simons

We propose an effective Lagrangian for the low energy theory of the Pfaffian states of the fractional quantum Hall effect in the bulk in terms of non-Abelian Chern–Simons (CS) actions. Our approach exploits the connection between the topological Chern–Simons theory and chiral conformal field theories. This construction can be used to describe a large class of non-Abelian FQH states.

scholarly journals Constructing Carrollian CFTs

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Nishant Gupta ◽  
Nemani V. Suryanarayana
Keyword(s):  
Scalar Fields ◽  
Higher Dimensions ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Relativistic Limit ◽  
Conformal Field ◽  
Local Symmetries ◽  
Derivatives Of ◽  
Special Case

Abstract We construct classical theories for scalar fields in arbitrary Carroll spacetimes that are invariant under Carrollian diffeomorphisms and Weyl transformations. When the local symmetries are gauge fixed these theories become Carrollian conformal field theories. We show that generically there are at least two types of such theories: one in which only time derivatives of the fields appear and the other in which both space and time derivatives appear. A classification of such scalar field theories in three (and higher) dimensions up to two derivative order is provided. We show that only a special case of our theories arises in the ultra-relativistic limit of a covariant parent theory.

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