scholarly journals THE CORRELATION FUNCTIONS OF THE (D4, A6) CONFORMAL MODEL

2004 ◽  
Vol 19 (25) ◽  
pp. 4271-4285
Author(s):  
S. BALASKA ◽  
K. DEMMOUCHE
Keyword(s):  
Correlation Functions ◽  
Conformal Algebra ◽  
Fusion Rules ◽  
Conformal Model ◽  
Structure Constants

In this work, we exploit the operator content of the (D4, A6) conformal algebra. By constructing a Z2-invariants fusion rules of a chosen subalgebra and by resolving the bootstrap equations consistent with these rules, we determine the structure constants of the subalgebra.

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 GALILEAN CONFORMAL ALGEBRA IN SEMI-INFINITE SPACE

2012 ◽  
Vol 27 (09) ◽  
pp. 1250044
Author(s):  
M. R. SETARE ◽  
V. KAMALI
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Correlation Functions ◽  
Fixed Time ◽  
Space Time ◽  
Conformal Algebra ◽  
Infinite Space ◽  
Conformal Algebras

In the present paper, we considered Galilean conformal algebras (GCAs), which arises as a contraction relativistic conformal algebras (xi→ϵxi, t→t, ϵ→0). We can use the Galilean conformal (GC) symmetry to constrain two-point and three-point functions. Correlation functions in space–time without boundary condition were found [A. Bagchi and I. Mandal, Phys. Lett. B675, 393 (2009).]. In real situations, there are boundary conditions in space–time, so we have calculated correlation functions for GC invariant fields in semi-infinite space with boundary condition in r = 0. We have calculated two-point and three-point functions with boundary condition in fixed time.

Some three-point correlation functions in the η-deformed AdS5 × S5

2016 ◽  
Vol 31 (01) ◽  
pp. 1550224 ◽  
Author(s):  
Plamen Bozhilov
Keyword(s):  
Field Theory ◽  
Angular Momentum ◽  
String Theory ◽  
Correlation Functions ◽  
Finite Size ◽  
Semiclassical Approach ◽  
Point Correlation ◽  
Structure Constants

We compute some normalized structure constants in the [Formula: see text]-deformed [Formula: see text] in the framework of the semiclassical approach. This is done for the cases when the “heavy” string states are finite-size giant magnons carrying one angular momentum and for three different choices of the “light” state: primary scalar operators, dilaton operator with nonzero momentum, singlet scalar operators on higher string levels. Since the dual field theory is still unknown, the results obtained here must be considered as conjectures or as predictions from the string theory side.

scholarly journals Analytic conformal bootstrap and Virasoro primary fields in the Ashkin-Teller model

2021 ◽  
Vol 11 (5) ◽  
Author(s):  
Nikita Nemkov ◽  
Sylvain Ribault
Keyword(s):  
Correlation Functions ◽  
Central Charge ◽  
Theta Functions ◽  
Conformal Dimension ◽  
Conformal Blocks ◽  
Conformal Bootstrap ◽  
Crossing Symmetry ◽  
Point Correlation ◽  
Structure Constants ◽  
Twist Fields

We revisit the critical two-dimensional Ashkin–Teller model, i.e. the \mathbb{Z}_2ℤ2 orbifold of the compactified free boson CFT at c=1c=1. We solve the model on the plane by computing its three-point structure constants and proving crossing symmetry of four-point correlation functions. We do this not only for affine primary fields, but also for Virasoro primary fields, i.e. higher twist fields and degenerate fields. This leads us to clarify the analytic properties of Virasoro conformal blocks and fusion kernels at c=1c=1. We show that blocks with a degenerate channel field should be computed by taking limits in the central charge, rather than in the conformal dimension. In particular, Al. Zamolodchikov’s simple explicit expression for the blocks that appear in four-twist correlation functions is only valid in the non-degenerate case: degenerate blocks, starting with the identity block, are more complicated generalized theta functions.

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 FUSION RESIDUES

1991 ◽  
Vol 06 (38) ◽  
pp. 3543-3556 ◽  
Author(s):  
KENNETH INTRILIGATOR
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Correlation Functions ◽  
Sigma Model ◽  
The Other ◽  
Necessary Condition ◽  
Fusion Rules ◽  
Conformal Field ◽  
Instanton Number

We discuss when and how the Verlinde dimensions of a rational conformal field theory can be expressed as correlation functions in a topological LG theory. It is seen that a necessary condition is that the RCFT fusion rules must exhibit an extra symmetry. We consider two particular perturbations of the Grassmannian superpotentials. The topological LG residues in one perturbation, introduced by Gepner are shown to be twisted version of the SU (N)k Verlinde dimensions. The residues in the other perturbation are the twisted Verlinde dimensions of another RCFT; these topological LG correlation functions are conjectured to be the correlation functions of the corresponding Grassmannian topological sigma model with a coupling in the action to instanton number.

scholarly journals CORRELATION FUNCTIONS OF THE TRI-CRITICAL 3-STATE POTTS MODEL

2004 ◽  
Vol 19 (28) ◽  
pp. 2135-2145
Author(s):  
S. BALASKA ◽  
K. DEMMOUCHE
Keyword(s):  
Integral Representation ◽  
Potts Model ◽  
Operator Algebra ◽  
Correlation Functions ◽  
The Other ◽  
Critical Fields ◽  
Conformal Blocks ◽  
Bootstrap Approach ◽  
Point Correlation ◽  
Structure Constants

We build the Z3 invariants fusion rules associated to the (D4,A6) conformal algebra. This algebra is known to describe the tri-critical Potts model. The 4-point correlation functions of critical fields are developed in the bootstrap approach, and on the other hand, they are written in terms of integral representation of the conformal blocks. By comparing both expressions, one can determine the structure constants of the operator algebra.

scholarly journals String correlators on AdS3: three-point functions

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Andrea Dei ◽  
Lorenz Eberhardt
Keyword(s):  
Correlation Functions ◽  
Spectral Flow ◽  
Closed Formula ◽  
Fusion Rules ◽  
First Time ◽  
String Worldsheet

Abstract We revisit the computation of string worldsheet correlators on Euclidean AdS3 with pure NS-NS background. We compute correlation functions with insertions of spectrally flowed operators. We explicitly solve all the known constraints of the model and for the first time conjecture a closed formula for three-point functions with arbitrary amount of spectral flow. We explain the relation of our results with previous computations in the literature and derive the fusion rules of the model. This paper is the first in a series with several installments.

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