scholarly journals BUILDING BLOCKS OF PHYSICAL STATES IN A NONCRITICAL 3-BRANE ON R × S3

2005 ◽  
Vol 20 (23) ◽  
pp. 5353-5398 ◽  
Author(s):  
KEN-JI HAMADA
Keyword(s):  
Conformal Transformation ◽  
Building Blocks ◽  
The Other ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Gravitational Fields ◽  
Conformally Invariant ◽  
Conformal Field ◽  
Special Conformal Transformation

The physical states in a worldvolume model of a noncritical 3-brane are systematically constructed using techniques of four-dimensional conformal field theories on R × S3 developed recently. Invariant combinations of creation modes under a special conformal transformation provide building blocks of physical states. Any state can be created by acting with such building blocks on a conformally invariant vacuum in an invariant way under the other conformal charges: the Hamiltonian and rotation generators on S3. We explicitly construct building blocks for scalar, vector and gravitational fields, and classify them as finite types.

INTEGRABLE LATTICE MODELS, GRAPHS AND MODULAR INVARIANT CONFORMAL FIELD THEORIES

1992 ◽  
Vol 07 (03) ◽  
pp. 407-500 ◽  
Author(s):  
P. DI FRANCESCO
Keyword(s):  
Lattice Models ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Compact Lie Groups ◽  
Modular Invariant ◽  
Conformally Invariant ◽  
Conformal Field ◽  
Integrable Lattice ◽  
Modular Invariants ◽  
Integrable Lattice Models

We review the construction of integrable height models attached to graphs, in connection with compact Lie groups. The continuum limit of these models yields conformally invariant field theories. A direct relation between graphs and (Kac–Moody or coset) modular invariants is proposed.

scholarly journals THE CAPPELLI–ITZYKSON–ZUBER A-D-E CLASSIFICATION

2000 ◽  
Vol 12 (05) ◽  
pp. 739-748 ◽  
Author(s):  
TERRY GANNON
Keyword(s):  
Mathematical Structure ◽  
The Other ◽  
Field Theories ◽  
Partition Functions ◽  
Conformal Field Theories ◽  
Modular Invariant ◽  
Conformal Field ◽  
Affine Algebras ◽  
Order Of Magnitude ◽  
The Rich

In 1986 Cappelli, Itzykson and Zuber classified all modular invariant partition functions for the conformal field theories associated to the affine A1 algebra; they found they fall into an A-D-E pattern. Their proof was difficult and attempts to generalise it to the other affine algebras failed — in hindsight the reason is that their argument ignored most of the rich mathematical structure present. We give here the "modern" proof of their result; it is an order of magnitude simpler and shorter, and much of it has already been extended to all other affine algebras. We conclude with some remarks on the A-D-E pattern appearing in this and other RCFT classifications.

NOVEL TOPOLOGICAL CONFORMAL ALGEBRAS

1991 ◽  
Vol 06 (14) ◽  
pp. 1321-1332 ◽  
Author(s):  
YOICHI KAZAMA
Keyword(s):  
Central Charge ◽  
The Other ◽  
Field Theories ◽  
Algebraic Characterization ◽  
Conformal Field Theories ◽  
Superconformal Symmetry ◽  
Conformal Field ◽  
Conformal Algebras ◽  
Slight Deformation

Algebraic characterization of 2-dimensional topological conformal field theories (TCFT’s) is proposed and some of its consequences are studied. In particular, we find two kinds of novel closed algebras, both of which are non-trivial extensions of the twisted version of the N=2 superconformal algebra. The larger of these algebras generically allows non-vanishing central charge c, a simple example of which is provided by a system with c=−2. The other algebra, on the other hand, requires vanishing central charge. An intriguing feature of this algebra is that it can be “untwisted” to yield a slight deformation of the N=2 algebra, which nevertheless possesses a hidden N=1 superconformal symmetry.

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 Entanglement and complexity of purification in ( 1+1 )-dimensional free conformal field theories

2021 ◽  
Vol 3 (1) ◽  
Author(s):  
Hugo A. Camargo ◽  
Lucas Hackl ◽  
Michal P. Heller ◽  
Alexander Jahn ◽  
Tadashi Takayanagi ◽  
...  
Keyword(s):  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field

scholarly journals NON-ABELIAN FRACTIONAL QUANTUM HALL STATES AND CHIRAL COSET CONFORMAL FIELD THEORIES

2000 ◽  
Vol 15 (30) ◽  
pp. 4857-4870 ◽  
Author(s):  
D. C. CABRA ◽  
E. FRADKIN ◽  
G. L. ROSSINI ◽  
F. A. SCHAPOSNIK
Keyword(s):  
Quantum Hall ◽  
Field Theories ◽  
Simons Theory ◽  
Conformal Field Theories ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Conformal Field ◽  
Quantum Hall States ◽  
Effective Lagrangian ◽  
Chern Simons

We propose an effective Lagrangian for the low energy theory of the Pfaffian states of the fractional quantum Hall effect in the bulk in terms of non-Abelian Chern–Simons (CS) actions. Our approach exploits the connection between the topological Chern–Simons theory and chiral conformal field theories. This construction can be used to describe a large class of non-Abelian FQH states.

scholarly journals Constructing Carrollian CFTs

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Nishant Gupta ◽  
Nemani V. Suryanarayana
Keyword(s):  
Scalar Fields ◽  
Higher Dimensions ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Relativistic Limit ◽  
Conformal Field ◽  
Local Symmetries ◽  
Derivatives Of ◽  
Special Case

Abstract We construct classical theories for scalar fields in arbitrary Carroll spacetimes that are invariant under Carrollian diffeomorphisms and Weyl transformations. When the local symmetries are gauge fixed these theories become Carrollian conformal field theories. We show that generically there are at least two types of such theories: one in which only time derivatives of the fields appear and the other in which both space and time derivatives appear. A classification of such scalar field theories in three (and higher) dimensions up to two derivative order is provided. We show that only a special case of our theories arises in the ultra-relativistic limit of a covariant parent theory.

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