NONLOCAL CURRENTS IN THE MASSIVE THIRRING MODEL

1993 ◽  
Vol 08 (10) ◽  
pp. 1815-1821 ◽  
Author(s):  
R.K. KAUL ◽  
R. RAJARAMAN
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Thirring Model ◽  
Massive Thirring Model ◽  
Conformal Field ◽  
Special Values ◽  
Fermion Number ◽  
Fermi Field ◽  
Conserved Currents

We derive nonlocal conserved currents in the massive Thirring model, treating the model as a perturbation on a conformal field theory. These currents carry fermion number two, and reduce to polynomials in the Fermi field for the special values of the Thirring coupling g=n/2.

scholarly journals Bounds on Regge growth of flat space scattering from bounds on chaos

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Deeksha Chandorkar ◽  
Subham Dutta Chowdhury ◽  
Suman Kundu ◽  
Shiraz Minwalla
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Flat Space ◽  
Gauge Fields ◽  
Point Singularity ◽  
Boundary Field ◽  
Conformal Field ◽  
S Matrix ◽  
Regge Limit ◽  
Conserved Currents

Abstract We study four-point functions of scalars, conserved currents, and stress tensors in a conformal field theory, generated by a local contact term in the bulk dual description, in two different causal configurations. The first of these is the standard Regge configuration in which the chaos bound applies. The second is the ‘causally scattering configuration’ in which the correlator develops a bulk point singularity. We find an expression for the coefficient of the bulk point singularity in terms of the bulk S matrix of the bulk dual metric, gauge fields and scalars, and use it to determine the Regge scaling of the correlator on the causally scattering sheet in terms of the Regge growth of this S matrix. We then demonstrate that the Regge scaling on this sheet is governed by the same power as in the standard Regge configuration, and so is constrained by the chaos bound, which turns out to be violated unless the bulk flat space S matrix grows no faster than s2 in the Regge limit. It follows that in the context of the AdS/CFT correspondence, the chaos bound applied to the boundary field theory implies that the S matrices of the dual bulk scalars, gauge fields, and gravitons obey the Classical Regge Growth (CRG) conjecture.

OPERATOR ALGEBRA IN TWO-DIMENSIONAL CONFORMAL FIELD THEORY CONTAINING SPIN 4/3 “PARAFERMIONIC” CONSERVED CURRENTS

1991 ◽  
Vol 06 (11) ◽  
pp. 2005-2023 ◽  
Author(s):  
R.H. POGHOSSIAN
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Operator Algebra ◽  
Closed Operator ◽  
Operator Product ◽  
Two Dimensional ◽  
Conformal Field ◽  
Structure Constants ◽  
Conserved Currents

Recently Zamolodchikov and Fateev have constructed a series of models of the two-dimensional conformal field theory containing spin 4/3 nonlocal (parafermion) currents. From degenerated fields one can construct a closed operator algebra with respect to the operator product expansions. All the structure constants of this algebra are computed in this paper.

scholarly journals Four-point correlation modular bootstrap for OPE densities

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Carlos Cardona ◽  
Cynthia Keeler ◽  
William Munizzi
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Spectral Decomposition ◽  
Large Dimension ◽  
Two Dimensional ◽  
Point Function ◽  
Conformal Field ◽  
Virasoro Symmetry ◽  
Point Correlation ◽  
Conserved Currents

Abstract In this work we apply the lightcone bootstrap to a four-point function of scalars in two-dimensional conformal field theory. We include the entire Virasoro symmetry and consider non-rational theories with a gap in the spectrum from the vacuum and no conserved currents. For those theories, we compute the large dimension limit (h/c ≫ 1) of the OPE spectral decomposition of the Virasoro vacuum. We then propose a kernel ansatz that generalizes the spectral decomposition beyond h/c ≫ 1. Finally, we estimate the corrections to the OPE spectral densities from the inclusion of the lightest operator in the spectrum.

A Review of Conformal Field Theory in 2D

2014 ◽  
Vol 6 (2) ◽  
pp. 1079-1105
Author(s):  
Rahul Nigam
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Conformal Field Theory ◽  
Statistical Mechanics ◽  
Critical Behavior ◽  
Verma Module ◽  
Virasoro Algebra ◽  
Quantum Field ◽  
Conformal Field ◽  
Insight Into

In this review we study the elementary structure of Conformal Field Theory in which is a recipe for further studies of critical behavior of various systems in statistical mechanics and quantum field theory. We briefly review CFT in dimensions which plays a prominent role for example in the well-known duality AdS/CFT in string theory where the CFT lives on the AdS boundary. We also describe the mapping of the theory from the cylinder to a complex plane which will help us gain an insight into the process of radial quantization and radial ordering. Finally we will develop the representation of the Virasoro algebra which is the well-known "Verma module".  

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 Decoherence in Conformal Field Theory

2020 ◽  
Vol 2020 (2) ◽  
Author(s):  
Adolfo del Campo ◽  
Tadashi Takayanagi
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Conformal Field

scholarly journals Parafermionization, bosonization, and critical parafermionic theories

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Yuan Yao ◽  
Akira Furusaki
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Degrees Of Freedom ◽  
Lattice Models ◽  
Partition Functions ◽  
Minimal Models ◽  
Fermionic Model ◽  
Conformal Field ◽  
Critical Theories ◽  
Wigner Transformation

AbstractWe formulate a ℤk-parafermionization/bosonization scheme for one-dimensional lattice models and field theories on a torus, starting from a generalized Jordan-Wigner transformation on a lattice, which extends the Majorana-Ising duality atk= 2. The ℤk-parafermionization enables us to investigate the critical theories of parafermionic chains whose fundamental degrees of freedom are parafermionic, and we find that their criticality cannot be described by any existing conformal field theory. The modular transformations of these parafermionic low-energy critical theories as general consistency conditions are found to be unconventional in that their partition functions on a torus transform differently from any conformal field theory whenk >2. Explicit forms of partition functions are obtained by the developed parafermionization for a large class of critical ℤk-parafermionic chains, whose operator contents are intrinsically distinct from any bosonic or fermionic model in terms of conformal spins and statistics. We also use the parafermionization to exhaust all the ℤk-parafermionic minimal models, complementing earlier works on fermionic cases.

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