MODULAR INVARIANT ONE-POINT CORRELATION FUNCTIONS FOR SU(2) WESS-ZUMINO MODEL

1992 ◽  
Vol 07 (25) ◽  
pp. 6257-6272 ◽  
Author(s):  
O.D. ANDREEV
Keyword(s):  
Correlation Functions ◽  
Riemann Surfaces ◽  
Free Field ◽  
Necessary Condition ◽  
Modular Invariant ◽  
Field Representation ◽  
Conformal Field ◽  
Higher Genus ◽  
Point Correlation ◽  
Zumino Model

We calculate one-point correlation functions of SU(2) Wess-Zumino model (WZM) on a torus using the Wakimoto free field representation. Their modular invariance is proved. It is a necessary condition of extending the WZ conformal field theory to higher genus Riemann surfaces.

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 Correlation Functions for Some Conformal Theories on Riemann Surfaces

1997 ◽  
Vol 12 (09) ◽  
pp. 589-596 ◽  
Author(s):  
Michael Monastyrsky ◽  
Sergei Nechaev
Keyword(s):  
Random Walks ◽  
Correlation Functions ◽  
Riemann Surfaces ◽  
Topological Invariants ◽  
Conformal Field Theories ◽  
Discrete Subgroups ◽  
Conformal Field ◽  
Point Correlation ◽  
Hyperbolic Riemann Surfaces

We discuss the geometrical connection between 2-D conformal field theories, random walks on hyperbolic Riemann surfaces and knot theory. For the wide class of CFTs with monodromies being the discrete subgroups of SL(2, ℝ), the determination of four-point correlation functions are related to construction of topological invariants for random walks on multipunctured Riemann surfaces.

Level-one SU(3) Wess-Zumino model on higher-genus Riemann surfaces

1990 ◽  
Vol 41 (2) ◽  
pp. 478-483 ◽  
Author(s):  
R. K. Kaul ◽  
R. P. Malik ◽  
N. Behera
Keyword(s):  
Riemann Surfaces ◽  
Higher Genus ◽  
Zumino Model

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.

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 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.

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