scholarly journals Categorification and correlation functions in conformal field theory

2009 ◽  
pp. 443-458 ◽  
Author(s):  
Christoph Schweigert ◽  
Jürgen Fuchs ◽  
Ingo Runkel
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Correlation Functions ◽  
Conformal Field

scholarly journals THE FREE FIELD REPRESENTATION OF SU(3) CONFORMAL FIELD THEORY

1993 ◽  
Vol 08 (23) ◽  
pp. 4031-4053
Author(s):  
HOVIK D. TOOMASSIAN
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Correlation Functions ◽  
Free Field ◽  
Field Representation ◽  
Conformal Field ◽  
Point Correlation

The structure of the free field representation and some four-point correlation functions of the SU(3) conformal field theory are considered.

scholarly journals Two point functions in defect CFTs

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Christopher P. Herzog ◽  
Abhay Shrestha
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Correlation Functions ◽  
Equations Of Motion ◽  
Physical Space ◽  
Arbitrary Spin ◽  
Momentum Tensor ◽  
Maxwell Theory ◽  
Conformal Field ◽  
Point Correlation

Abstract This paper is designed to be a practical tool for constructing and investigating two-point correlation functions in defect conformal field theory, directly in physical space, between any two bulk primaries or between a bulk primary and a defect primary, with arbitrary spin. Although geometrically elegant and ultimately a more powerful approach, the embedding space formalism gets rather cumbersome when dealing with mixed symmetry tensors, especially in the projection to physical space. The results in this paper provide an alternative method for studying two-point correlation functions for a generic d-dimensional conformal field theory with a flat p-dimensional defect and d − p = q co-dimensions. We tabulate some examples of correlation functions involving a conserved current, an energy momentum tensor and a Maxwell field strength, while analysing the constraints arising from conservation and the equations of motion. A method for obtaining bulk-to-defect correlators is also explained. Some explicit examples are considered: free scalar theory on ℝp× (ℝq/ℤ2) and a free four dimensional Maxwell theory on a wedge.

scholarly journals SU(2)k×SU(2)l/SU(2)k+l COSET CONFORMAL FIELD THEORY AND TOPOLOGICAL MINIMAL MODEL ON HIGHER GENUS RIEMANN SURFACE

1993 ◽  
Vol 08 (31) ◽  
pp. 5537-5561 ◽  
Author(s):  
HITOSHI KONNO
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Riemann Surface ◽  
Vertex Operator ◽  
Correlation Functions ◽  
Minimal Model ◽  
The Other ◽  
Operator Formalism ◽  
Conformal Field ◽  
Higher Genus

We consider the Feigin-Fuchs-Felder formalism of the SU (2)k× SU (2)l/ SU (2)k+l coset minimal conformal field theory and extend it to higher genus. We investigate a double BRST complex with respect to two compatible BRST charges, one associated with the parafermion sector and the other associated with the minimal sector in the theory. The usual screened vertex operator is extended to the BRST-invariant screened three-string vertex. We carry out a sewing operation of these vertices and derive the BRST-invariant screened g-loop operator. The latter operator characterizes the higher genus structure of the theory. An analogous operator formalism for the topological minimal model is obtained as the limit l=0 of the coset theory. We give some calculations of correlation functions on higher genus.

scholarly journals Logarithmic Operators in Conformal Field Theory and the ${\mathcal W}_\infty$-Algebra

1997 ◽  
Vol 12 (21) ◽  
pp. 3723-3738 ◽  
Author(s):  
A. Shafiekhani ◽  
M. R. Rahimi Tabar
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Correlation Functions ◽  
Operator Product Expansion ◽  
Field Theories ◽  
Operator Product ◽  
Tensor Operator ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Point Correlation

It is shown explicitly that the correlation functions of conformal field theories (CFT) with the logarithmic operators are invariant under the differential realization of Borel subalgebra of [Formula: see text]-algebra. This algebra is constructed by tensor-operator algebra of differential representation of ordinary [Formula: see text]. This method allows us to write differential equations which can be used to find general expression for three- and four-point correlation functions possessing logarithmic operators. The operator product expansion (OPE) coefficients of general logarithmic CFT are given up to third level.

scholarly journals CONFORMAL INVARIANCE ON ORBIFOLDS AND EXCITATIONS OF SINGULARITY

2009 ◽  
Vol 24 (26) ◽  
pp. 2089-2097 ◽  
Author(s):  
ZHENG YIN
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Correlation Functions ◽  
Conformal Invariance ◽  
Two Dimensional ◽  
Conformal Field ◽  
Boundary States ◽  
Physical Effects

We study conformal field theory on two-dimensional orbifolds and show this to be an effective way to analyze physical effects of geometric singularities with angular deficits. They are closely related to boundaries and cross caps. Representative classes of singularities can be described exactly using generalizations of boundary states. From this we compute correlation functions and derive the spectra of excitations localized at the singularities.

INTERACTING BOSONIC MODELS AND THEIR SOLUTION

1991 ◽  
Vol 06 (24) ◽  
pp. 2249-2258 ◽  
Author(s):  
RON COHEN ◽  
DORON GEPNER
Keyword(s):  
Field Theory ◽  
Exact Solution ◽  
Conformal Field Theory ◽  
Large Class ◽  
Infinite Number ◽  
Correlation Functions ◽  
Central Charge ◽  
Conformal Field

A family of interacting bosonic models is studied. A picture is suggested where each such conformal field theory is tensored with a conjugate one to give a free bosonic theory. It is shown that the lattice of the bosonic theory is determined in each case, and how the spectrum and correlation functions can be calculated. It is explained how flat directions can arise in such theories, allowing for an exact solution for a family of parameters. A large class of examples is discussed in detail. It is shown that for any rational value of the central charge c ≥ 3 there is an infinite number of distinct rational N = 2 theories which can be contracted by this method.

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