HIGHER SPIN SYMMETRY AND SU(2) WZNW MODEL

1994 ◽  
Vol 09 (26) ◽  
pp. 2389-2398
Author(s):  
SASANKA GHOSH
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Ising Model ◽  
Higher Spin Symmetry ◽  
Symmetry Algebra ◽  
Spin Symmetry ◽  
Conformal Field ◽  
Large N ◽  
Wznw Model ◽  
Higher Spin

Generators of an infinite number of conserved charges of the integrable SU(2) WZNW model are identified with the generators of a W1+∞ symmetry algebra. This integrable conformal field theory also describes the ZN symmetric Ising model at the critical point in the large-N limit.

scholarly journals Four point functions in CFT’s with slightly broken higher spin symmetry

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Joao A. Silva
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Higher Spin Symmetry ◽  
Three Dimensional ◽  
Spin Current ◽  
Spin Symmetry ◽  
Trace Operator ◽  
Conformal Field ◽  
Higher Spin ◽  
Single Trace

Abstract We compute spinning four point functions in the quasi-fermionic three dimensional conformal field theory with slightly broken higher spin symmetry at finite t’Hooft coupling. More concretely, we obtain a formula for $$ \left\langle {j}_s{j}_{\tilde{0}}{j}_{\tilde{0}}{j}_{\tilde{0}}\right\rangle $$ j s j 0 ˜ j 0 ˜ j 0 ˜ , where js is a higher spin current and $$ {j}_{\tilde{0}} $$ j 0 ˜ is the scalar single trace operator. Our procedure consists in writing a plausible ansatz in Mellin space and using crossing, pseudo-conservation and Regge boundedness to fix all undetermined coefficients. Our method can potentially be generalised to compute all spinning four point functions in these theories.

scholarly journals Chern-Simons gravity dual of BCFT

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Tadashi Takayanagi ◽  
Takahiro Uetoko
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Entanglement Entropy ◽  
Einstein Gravity ◽  
Conformal Field ◽  
Holographic Entanglement Entropy ◽  
The World ◽  
Higher Spin ◽  
End Of The World ◽  
Chern Simons

Abstract In this paper we provide a Chern-Simons gravity dual of a two dimensional conformal field theory on a manifold with boundaries, so called boundary conformal field theory (BCFT). We determine the correct boundary action on the end of the world brane in the Chern-Simons gauge theory. This reproduces known results of the AdS/BCFT for the Einstein gravity. We also give a prescription of calculating holographic entanglement entropy by employing Wilson lines which extend from the AdS boundary to the end of the world brane. We also discuss a higher spin extension of our formulation.

scholarly journals TOWARD A CONFORMAL FIELD THEORY FOR THE QUANTUM HALL EFFECT

1992 ◽  
Vol 06 (19) ◽  
pp. 3235-3247
Author(s):  
GREG NAGAO
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Order Parameter ◽  
Quantum Hall ◽  
Cyclotron Motion ◽  
Conformal Field ◽  
Large N ◽  
Collective Coordinate

An effective Hamiltonian for the study of the quantum Hall effect is proposed. This Hamiltonian, which includes a "current-current" interaction has the form of a Hamiltonian for a conformal field theory in the large N limit. An order parameter is constructed from which the Hamiltonian may be derived. This order parameter may be viewed as either a collective coordinate for a system of N charged particles in a strong magnetic field; or as a field of spins associated with the cyclotron motion of these particles.

RESHETIKHIN-TURAEV AND CRANE-KOHNO-KONTSEVICH 3-MANIFOLD INVARIANTS COINCIDE

1993 ◽  
Vol 02 (01) ◽  
pp. 65-95 ◽  
Author(s):  
SERGEY PIUNIKHIN
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Explicit Formula ◽  
Quantum Groups ◽  
Jones Polynomial ◽  
Matrix Elements ◽  
Conformal Blocks ◽  
Conformal Field ◽  
Wznw Model ◽  
The Matrix

The coincidence of two different presentations of Witten 3-manifold invariants is proved. One of them, invented by Reshetikhin and Turaev, is based on the surgery presentation a of 3-manifold and the representation theory of quantum groups; another one, invented by Kohno and Crane and, in slightly different language by Kontsevich, is based on a Heegaard decomposition of a 3-manifold and representations of the Teichmuller group, arising in conformal field theory. The explicit formula for the matrix elements of generators of the Teichmuller group in the space of conformal blocks in the SU(2) k, WZNW-model is given,using the Jones polynomial of certain links.

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