scholarly journals DUAL GENERALIZATIONS OF SINE–GORDON FIELD THEORY AND INTEGRABILITY SUBMANIFOLDS IN PARAMETER SPACE

2000 ◽  
Vol 15 (21) ◽  
pp. 3315-3340
Author(s):  
P. BASEILHAC ◽  
D. REYNAUD
Keyword(s):  
Field Theory ◽  
Parameter Space ◽  
Complex Space ◽  
Central Charge ◽  
Two Dimensions ◽  
Field Theories ◽  
Complex Numbers ◽  
Quantum Field Theories ◽  
Conformal Field ◽  
Extended Complex

The dual relationship between two n-1 parameter families of quantum field theories based on extended complex numbers is investigated in two dimensions. The nonlocal conserved charges approach is used. The lowest rank affine Toda field theories are generated and identified as integrability submanifolds in parameter space. A truncation of the model leads to a conformal field theory in extended complex space. Depending on the projection over the usual complex space chosen, a parametrized central charge is calculated.

scholarly journals HIDDEN SYMMETRIES IN QUANTUM FIELD THEORIES FROM EXTENDED COMPLEX NUMBERS

1999 ◽  
Vol 14 (26) ◽  
pp. 4201-4235 ◽  
Author(s):  
PASCAL BASEILHAC
Keyword(s):  
Field Theory ◽  
Dimensional Space ◽  
Field Theories ◽  
Complex Numbers ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Hidden Symmetries ◽  
Dimensional Space Time ◽  
Extended Complex ◽  
Dual Models

The two-dimensional space–time sine–Gordon field theory is extended algebraically within the n-dimensional space of extended complex numbers. This field theory is constructed in terms of an adapted extension of standard vertex operators. A whole set of nonlocal conserved charges is constructed and studied in this framework. Thereby, an algebraic nonperturbative description is possible for this n-1 parameters family of quantum field theories. Known results are obtained for specific values of the parameters, especially in relation to affine Toda field theories. Different (dual)-models can then be described in this formalism.

scholarly journals M$_k$ models: the field theory connection

2017 ◽  
Vol 3 (1) ◽  
Author(s):  
Thessa Fokkema ◽  
Kareljan Schoutens
Keyword(s):  
Field Theory ◽  
Finite Size ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Minimal Models ◽  
Size Spectra ◽  
Conformal Field ◽  
Lattice Fermions ◽  
Clustering Property

The M_kk models for 1D lattice fermions are characterised by {\cal N}=2 supersymmetry and by an order-kk clustering property. This paper highlights connections with quantum field theories (QFTs) in various regimes. At criticality the QFTs are minimal models of {\cal N}=2 supersymmetric conformal field theory (CFT) - we analyse finite size spectra on open chains with a variety of supersymmetry preserving boundary conditions. Specific staggering perturbations lead to a gapped regime corresponding to massive {\cal N}=2 supersymmetric QFT with Chebyshev superpotentials. At ‘extreme staggering’ we uncover a simple physical picture with degenerate supersymmetric vacua and mobile kinks. We connect this kink-picture to the Chebyshev QFTs and use it to derive novel CFT character formulas. For clarity the focus in this paper is on the simplest models, M_11, M_22 and M_33.

ELASTIC S-MATRICES IN (1 + 1) DIMENSIONS AND TODA FIELD THEORIES

1990 ◽  
Vol 05 (24) ◽  
pp. 4581-4627 ◽  
Author(s):  
P. CHRISTE ◽  
G. MUSSARDO
Keyword(s):  
Field Theory ◽  
General Scheme ◽  
Field Theories ◽  
Scattering Data ◽  
Quantum Field Theories ◽  
Conformal Field ◽  
Dynkin Diagrams ◽  
S Matrix ◽  
Relativistic Scattering ◽  
Toda Field Theory

Particular deformations of 2-D conformal field theory lead to integrable massive quantum field theories. These can be characterized by the relativistic scattering data. We propose a general scheme for classifying the elastic nondegenerate S-matrix in (1 + 1) dimensions starting from the possible boot-strap processes and the spins of the conserved currents. Their identification with the S-matrix coming from the Toda field theory is analyzed. We discuss both cases of Toda field theory constructed with the simply-laced Dynkin diagrams and the nonsimply-laced ones. We present the results of the perturbative analysis and their geometrical interpretations.

scholarly journals Analysis for Lorentzian conformal field theories through sine-square deformation

2020 ◽  
Vol 2020 (6) ◽  
Author(s):  
Xun Liu ◽  
Tsukasa Tada
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Continuous Spectrum ◽  
Central Charge ◽  
Virasoro Algebra ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
The Third

Abstract We reexamine two-dimensional Lorentzian conformal field theory using the formalism previously developed in a study of sine-square deformation of Euclidean conformal field theory. We construct three types of Virasoro algebra. One of them reproduces the result by Lüscher and Mack, while another type exhibits divergence in the central charge term. The third leads to a continuous spectrum and contains no closed time-like curve in the system.

scholarly journals a – c test of holography versus quantum renormalization group

2014 ◽  
Vol 29 (29) ◽  
pp. 1450158 ◽  
Author(s):  
Yu Nakayama
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Conformal Field Theory ◽  
Beta Function ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
De Sitter ◽  
Conformal Field ◽  
Large N

We show that a "constructive derivation" of the anti-de Sitter/conformal field theory (AdS/CFT) correspondence based on the quantum local renormalization group in large-N quantum field theories consistently provides the a – c holographic Weyl anomaly in d = 4 at the curvature squared order in the bulk action. The consistency of the construction further predicts the form of the metric beta function.

CONFORMAL FIELD THEORY AND PURELY ELASTIC S-MATRICES

1990 ◽  
Vol 05 (06) ◽  
pp. 1025-1048 ◽  
Author(s):  
V.A. FATEEV ◽  
A.B. ZAMOLODCHIKOV
Keyword(s):  
Magnetic Field ◽  
Field Theory ◽  
Conformal Field Theory ◽  
Mass Spectra ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Potts Models ◽  
Conformal Field ◽  
Toda Systems

Particular perturbations of a 2D Conformal Field Theory leading to Integrable massive Quantum Field Theories are examined. The mass spectra and S-matrices for some models, including the field theory of the Ising Model with magnetic field and “thermal” deformations of the tricritical Ising and 3-state Potts models, are proposed. The hidden Lie-algebraic structures of these spectra and their relation to the Toda systems are discussed.

scholarly journals Cutoff AdS3 versus $$ T\overline{T} $$ CFT2 in the large central charge sector: correlators of energy-momentum tensor

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Yi Li ◽  
Yang Zhou
Keyword(s):  
Field Theory ◽  
Euclidean Plane ◽  
Energy Momentum Tensor ◽  
Central Charge ◽  
Momentum Tensor ◽  
Two Dimensional ◽  
Conformal Field ◽  
Operator Identity ◽  
Pure Gravity ◽  
Charge Sector

Abstract In this article we probe the proposed holographic duality between $$ T\overline{T} $$ T T ¯ deformed two dimensional conformal field theory and the gravity theory of AdS3 with a Dirichlet cutoff by computing correlators of energy-momentum tensor. We focus on the large central charge sector of the $$ T\overline{T} $$ T T ¯ CFT in a Euclidean plane and a sphere, and compute the correlators of energy-momentum tensor using an operator identity promoted from the classical trace relation. The result agrees with a computation of classical pure gravity in Euclidean AdS3 with the corresponding cutoff surface, given a holographic dictionary which identifies gravity parameters with $$ T\overline{T} $$ T T ¯ CFT parameters.

THE ANNIHILATING IDEALS OF MINIMAL MODELS

1992 ◽  
Vol 07 (supp01a) ◽  
pp. 217-238 ◽  
Author(s):  
BORIS L. FEIGIN ◽  
TOMOKI NAKANISHI ◽  
HIROSI OOGURI
Keyword(s):  
Central Charge ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Finite Models ◽  
Conformal Field ◽  
Intimate Relation ◽  
Chiral Algebras

We describe several aspects of the annihilating ideals and reduced chiral algebras of conformal field theories, especially, minimal models of Wn algebras. The structure of the annihilating ideal and a vanishing condition is given. Using the annihilating ideal, the structure of quasi-finite models of the Virasoro (2,q) minimal models are studied, and their intimate relation to the Gordon identities are discussed. We also show the examples in which the reduced algebras of Wn and Wℓ algebras at the same central charge are isomorphic to each other.

scholarly journals Construction and classification of holomorphic vertex operator algebras

2020 ◽  
Vol 2020 (759) ◽  
pp. 61-99 ◽  
Author(s):  
Jethro van Ekeren ◽  
Sven Möller ◽  
Nils R. Scheithauer
Keyword(s):  
Vertex Operator ◽  
Operator Algebras ◽  
Central Charge ◽  
Field Theories ◽  
Vertex Operator Algebras ◽  
Conformal Field Theories ◽  
Cyclic Groups ◽  
Conformal Field

AbstractWe develop an orbifold theory for finite, cyclic groups acting on holomorphic vertex operator algebras. Then we show that Schellekens’ classification of {V_{1}}-structures of meromorphic conformal field theories of central charge 24 is a theorem on vertex operator algebras. Finally, we use these results to construct some new holomorphic vertex operator algebras of central charge 24 as lattice orbifolds.

scholarly journals Instability of complex CFTs with operators in the principal series

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Dario Benedetti
Keyword(s):  
Principal Series ◽  
Conformal Group ◽  
Point Of View ◽  
Field Theories ◽  
Operator Product ◽  
Quantum Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Primary Operator ◽  
Tensor Models

Abstract We prove the instability of d-dimensional conformal field theories (CFTs) having in the operator-product expansion of two fundamental fields a primary operator of scaling dimension h = $$ \frac{d}{2} $$ d 2 + i r, with non-vanishing r ∈ ℝ. From an AdS/CFT point of view, this corresponds to a well-known tachyonic instability, associated to a violation of the Breitenlohner-Freedman bound in AdSd+1; we derive it here directly for generic d-dimensional CFTs that can be obtained as limits of multiscalar quantum field theories, by applying the harmonic analysis for the Euclidean conformal group to perturbations of the conformal solution in the two-particle irreducible (2PI) effective action. Some explicit examples are discussed, such as melonic tensor models and the biscalar fishnet model.

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