scholarly journals (p, q)-Analog of Two-Dimensional Conformal Field Theory. The Ward Identities and Correlation Functions

1995 ◽  
Vol 2 (2) ◽  
pp. 114-119 ◽  
Author(s):  
I.M. Burban
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Correlation Functions ◽  
Two Dimensional ◽  
Ward Identities ◽  
Conformal Field

scholarly journals Minimal lectures on two-dimensional conformal field theory

2018 ◽  
Author(s):  
Sylvain Ribault
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Conformal Invariance ◽  
Existence And Uniqueness ◽  
Riemann Sphere ◽  
Liouville Theory ◽  
Two Dimensional ◽  
Minimal Models ◽  
Ward Identities ◽  
Conformal Field

We provide a brief but self-contained review of conformal field theory on the Riemann sphere. We first introduce general axioms such as local conformal invariance, and derive Ward identities and BPZ equations. We then define minimal models and Liouville theory by specific axioms on their spectrums and degenerate fields. We solve these theories by computing three- and four-point functions, and discuss their existence and uniqueness.

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.

TWO-DIMENSIONAL QUANTUM GRAVITY ON A DISK

1992 ◽  
Vol 07 (06) ◽  
pp. 521-532 ◽  
Author(s):  
YOSHIAKI TANII ◽  
SHUN-ICHI YAMAGUCHI
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Quantum Gravity ◽  
Correlation Functions ◽  
Two Dimensional ◽  
Field Approach ◽  
Conformal Field ◽  
Boundary Operators ◽  
Point Correlation ◽  
The Continuum

We study a two-dimensional conformal field theory coupled to quantum gravity on a disk. Using the continuum Liouville field approach, we compute three-point correlation functions of boundary operators. The structure of momentum singularities is different from that of correlation functions on a sphere and is more complicated. We also compute four-point functions of boundary operators and three-point functions of two boundary operators and one bulk operator.

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 Symmetry-resolved entanglement in AdS3/CFT2 coupled to U(1) Chern-Simons theory

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Suting Zhao ◽  
Christian Northe ◽  
René Meyer
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Gauge Field ◽  
Wilson Line ◽  
Entanglement Entropy ◽  
Simons Theory ◽  
Two Dimensional ◽  
Conformal Field ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We consider symmetry-resolved entanglement entropy in AdS3/CFT2 coupled to U(1) Chern-Simons theory. We identify the holographic dual of the charged moments in the two-dimensional conformal field theory as a charged Wilson line in the bulk of AdS3, namely the Ryu-Takayanagi geodesic minimally coupled to the U(1) Chern-Simons gauge field. We identify the holonomy around the Wilson line as the Aharonov-Bohm phases which, in the two-dimensional field theory, are generated by charged U(1) vertex operators inserted at the endpoints of the entangling interval. Furthermore, we devise a new method to calculate the symmetry resolved entanglement entropy by relating the generating function for the charged moments to the amount of charge in the entangling subregion. We calculate the subregion charge from the U(1) Chern-Simons gauge field sourced by the bulk Wilson line. We use our method to derive the symmetry-resolved entanglement entropy for Poincaré patch and global AdS3, as well as for the conical defect geometries. In all three cases, the symmetry resolved entanglement entropy is determined by the length of the Ryu-Takayanagi geodesic and the Chern-Simons level k, and fulfills equipartition of entanglement. The asymptotic symmetry algebra of the bulk theory is of $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody type. Employing the $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody symmetry, we confirm our holographic results by a calculation in the dual conformal field theory.

scholarly journals Four-dimensional conformal field theory models with rational correlation functions

2002 ◽  
Vol 35 (12) ◽  
pp. 2985-3007 ◽  
Author(s):  
N M Nikolov ◽  
Ya S Stanev ◽  
I T Todorov
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Correlation Functions ◽  
Conformal Field

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.

POISSON–LIE GROUPS AND CLASSICAL W-ALGEBRAS

1992 ◽  
Vol 07 (05) ◽  
pp. 853-876 ◽  
Author(s):  
V. A. FATEEV ◽  
S. L. LUKYANOV
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Quantum Group ◽  
Lie Groups ◽  
Group Structure ◽  
Two Dimensional ◽  
Poisson Structures ◽  
Additional Symmetries ◽  
Conformal Field ◽  
Poisson Lie Groups

This is the first part of a paper studying the quantum group structure of two-dimensional conformal field theory with additional symmetries. We discuss the properties of the Poisson structures possessing classical W-invariance. The Darboux variables for these Poisson structures are constructed.

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