SUPERSELECTION SECTORS WITH BRAID GROUP STATISTICS AND EXCHANGE ALGEBRAS II: GEOMETRIC ASPECTS AND CONFORMAL COVARIANCE

1992 ◽  
Vol 04 (spec01) ◽  
pp. 113-157 ◽  
Author(s):  
KLAUS FREDENHAGEN ◽  
KARL-HENNING REHREN ◽  
BERT SCHROER
Keyword(s):  
Braid Group ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Cpt Symmetry ◽  
Conformal Field ◽  
Exchange Algebra ◽  
Braid Group Statistics ◽  
Almost All ◽  
Conformal Covariance

The general theory of superselection sectors is shown to provide almost all the structure observed in two-dimensional conformal field theories. Its application to two-dimensional conformally covariant and three-dimensional Poincaré covariant theories yields a general spin-statistics connection previously encountered in more special situations. CPT symmetry can be shown also in the absence of local (anti-) commutation relations, if the braid group statistics is expressed in the form of an exchange algebra.

scholarly journals MULTIVALUED FIELDS ON THE COMPLEX PLANE AND BRAID GROUP STATISTICS

1994 ◽  
Vol 09 (03) ◽  
pp. 313-325 ◽  
Author(s):  
FRANCO FERRARI
Keyword(s):  
Riemann Surface ◽  
Complex Plane ◽  
Riemann Surfaces ◽  
Conformal Field Theories ◽  
Local Exchange ◽  
R Matrix ◽  
Conformal Field ◽  
Exchange Algebra ◽  
Braid Group Statistics ◽  
Nontrivial Topology

In this paper we study a class of theories of free particles on the complex plane satisfying a non-Abelian statistics. This kind of particles are generalizations of the anyons and are sometimes called plectons. The peculiarity of these theories is that they are associated to free conformal field theories defined on Riemann surfaces with a discrete and non-Abelian group of authomorphisms Dm. More explicitly, the plectons appear here as “induced vertex operators” that simulate, on the complex plane, the nontrivial topology of the Riemann surface. In order to express the local exchange algebra of the particles, one is led to introduce an R matrix satisfying a multiparameter generalization of the usual Yang-Baxter equations. It is interesting that analogous generalizations have already been investigated in connection with integrable models, in which the spectral parameter takes its values on a Riemann surface that is in many respects similar to the Riemann surfaces we are studying here. The explicit form of the R matrices mentioned above can be also used to define a multiparameter version of the quantum complex hyperplane.

scholarly journals GENERALIZED ABELIAN CHERN-SIMONS THEORIES AND THEIR CONNECTION TO CONFORMAL FIELD THEORIES

1992 ◽  
Vol 07 (19) ◽  
pp. 4477-4486 ◽  
Author(s):  
MARCO A.C. KNEIPP
Keyword(s):  
Three Dimensional ◽  
Magnetic Monopoles ◽  
Field Theories ◽  
Vertex Operators ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Integral Lattice ◽  
Conformal Field ◽  
Free Scalar ◽  
Chern Simons

We discuss the generalization of Abelian Chern-Simons theories when θ-angles and magnetic monopoles are included. We map these three dimensional theories into sectors of two-dimensional conformal field theories. The introduction of θ-angles allows us to establish in a consistent fashion a connection between Abelian Chern-Simons and 2-d free scalar field compactified on a noneven integral lattice. The Abelian Chern-Simons with magnetic monopoles is related to a conformal field theory in which the sum of the charges of the chiral vertex operators inside a correlator is different from zero.

scholarly journals Gravitational Dressing of Aharonov-Bohm Amplitudes

1997 ◽  
Vol 12 (06) ◽  
pp. 1043-1051 ◽  
Author(s):  
Giovanni Amelino-Camelia ◽  
Ian I. Kogan ◽  
Richard J. Szabo
Keyword(s):  
Three Dimensional ◽  
Matter Field ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Gravitational Analog ◽  
Bohm Effect ◽  
Aharonov Bohm ◽  
Chern Simons

We investigate Aharonov-Bohm scattering in a theory in which charged bosonic matter field are coupled to topologically massive electrodynamics and topologically massive gravity. We demonstrate that, at one-loop order, the transmuted spins in this theory are related to the ones of ordinary Chern-Simons gauge theory in the same way that the Knizhnik-Polyakov-Zamolodchikov formula relates the Liouville-dressed conformal weights of primary operators to the bare weights of primary operators to the bare weights in two-dimensional conformal field theories. We remark on the implications of this connection two-dimensional conformal field theories and three-dimensional gauge and gravity theories for a topological membrane reformulation of strings. We also discuss some features of the gravitational analog of the Aharonov-Bohm effect.

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 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.

Chiral modular bootstrap

2019 ◽  
Vol 34 (28) ◽  
pp. 1950168 ◽  
Author(s):  
M. Ashrafi
Keyword(s):  
Black Hole ◽  
Upper Bound ◽  
Three Dimensional ◽  
Conformal Weight ◽  
Two Dimensional ◽  
Btz Black Hole ◽  
Conformal Field ◽  
Dimensional Gravity ◽  
Large Spin ◽  
Dimension Ratio

Using modular bootstrap we show the lightest primary fields of a unitary compact two-dimensional conformal field theory (with [Formula: see text], [Formula: see text]) has a conformal weight [Formula: see text]. This implies that the upper bound on the dimension of the lightest primary fields depends on their spin. In particular if the set of lightest primary fields includes extremal or near extremal states whose spin to dimension ratio [Formula: see text], the corresponding dimension is [Formula: see text]. From AdS/CFT correspondence, we obtain an upper bound on the spectrum of black hole in three-dimensional gravity. Our results show that if the first primary fields have large spin, the corresponding three-dimensional gravity has extremal or near extremal BTZ black hole.

CONFORMAL THEORIES, CURVED PHASE SPACES, RELATIVISTIC WAVELETS AND THE GEOMETRY OF COMPLEX DOMAINS

1990 ◽  
Vol 02 (01) ◽  
pp. 1-44 ◽  
Author(s):  
R. COQUEREAUX ◽  
A. JADCZYK
Keyword(s):  
General Relativity ◽  
Complex Geometry ◽  
Three Dimensional ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Relativistic Phase

We investigate some aspects of complex geometry in relation with possible applications to quantization, relativistic phase spaces, conformal field theories, general relativity and the music of two and three-dimensional spheres.

Sign in / Sign up

Export Citation Format

Share Document