scholarly journals SL(2, Z) ACTION ON THREE-DIMENSIONAL CONFORMAL FIELD THEORIES WITH ABELIAN SYMMETRY

2005 ◽  
pp. 1173-1200 ◽  
Author(s):  
EDWARD WITTEN
Keyword(s):  
Three Dimensional ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field

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.

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.

MATHEMATICA™ PACKAGES FOR COMPUTING PRINCIPAL DECOMPOSITIONS OF SIMPLE LIE ALGEBRAS AND APPLICATIONS IN EXTENDED CONFORMAL FIELD THEORIES

2003 ◽  
Vol 14 (01) ◽  
pp. 1-27 ◽  
Author(s):  
DANIELA GĂRĂJEU ◽  
MIHAIL GĂRĂJEU
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Three Dimensional ◽  
Adjoint Representation ◽  
Cartan Matrix ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Killing Form ◽  
Simple Lie Algebras ◽  
Conformal Field

In this article, we propose two Mathematica™ packages for doing calculations in the domain of classical simple Lie algebras. The main goal of the first package, [Formula: see text], is to determine the principal three-dimensional subalgebra of a simple Lie algebra. The package provides several functions which give some elements related to simple Lie algebras (generators in fundamental and adjoint representation, roots, Killing form, Cartan matrix, etc.). The second package, [Formula: see text], concerns the principal decomposition of a Lie algebra with respect to the principal three-dimensional embedding. These packages have important applications in extended two-dimensional conformal field theories. As an example, we present an application in the context of the theory of W-gravity.

scholarly journals Holographic entanglement entropy in cutoff AdS

2018 ◽  
Vol 33 (36) ◽  
pp. 1850226 ◽  
Author(s):  
Chanyong Park
Keyword(s):  
Fixed Point ◽  
Entanglement Entropy ◽  
Three Dimensional ◽  
Energy Scale ◽  
Field Theories ◽  
Dimensional Sphere ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Holographic Entanglement Entropy ◽  
Length Contraction

We investigate the holographic entanglement entropy of deformed conformal field theories which are dual to a cutoff AdS space. The holographic entanglement entropy evaluated on a three-dimensional Poincaré AdS space with a finite cutoff can be reinterpreted as that of the dual field theory deformed by either a boost or [Formula: see text] deformation. For the boost case, we show that, although it trivially acts on the underlying theory, it nontrivially affects the entanglement entropy due to the length contraction. For a three-dimensional AdS, we show that the effect of the boost transformation can be reinterpreted as the rescaling of the energy scale, similar to the [Formula: see text] deformation. Under the boost and [Formula: see text] deformation, the [Formula: see text]-function of the entanglement entropy exactly shows the features expected by the Zamolodchikov’s [Formula: see text]-theorem. The deformed theory is always stationary at a UV fixed point and monotonically flows to another CFT in the IR fixed point. We also show that the holographic entanglement entropy in a Poincaré cutoff AdS space can reproduce the exact same result of the [Formula: see text] deformed theory on a two-dimensional sphere.

scholarly journals Non-Supersymmetric CS-Matter Theories with Known AdS Duals

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Davide Forcella ◽  
Alberto Zaffaroni
Keyword(s):  
Field Theory ◽  
Three Dimensional ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Natural Field ◽  
Conformal Field ◽  
Stable Field ◽  
Supergravity Solution

We consider three-dimensional conformal field theories living on a stack ofNanti-M2 branes at the tip of eight-dimensional supersymmetric cones. The corresponding supergravity solution is obtained by changing sign to the four-form in the Freund-Rubin solution representing M2 branes (“skew-whiffing” transformation) and it is known to be stable. The existence of these non-supersymmetric, stable field theories, at least in the largeNlimit, is a peculiarity of theAdS4/CFT3correspondence with respect to the usualAdS5/CFT4, and it is worthwhile to study it. We analyze in detail the KK spectrum of the skew-whiffed solution associated withS7/ℤkand we speculate on the natural field content for a candidate non-supersymmetric dual field theory.

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.

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