Graphs, algebras, conformal field theories and integrable lattice models

1991 ◽  
Vol 18 (2) ◽  
pp. 313-326 ◽  
Author(s):  
J.-B. Zuber
Keyword(s):  
Lattice Models ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Integrable Lattice ◽  
Integrable Lattice Models

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 ON STATE COUNTING AND CHARACTERS

1995 ◽  
Vol 10 (06) ◽  
pp. 875-894 ◽  
Author(s):  
SRINANDAN DASMAHAPATRA
Keyword(s):  
Lattice Models ◽  
Field Theories ◽  
Bethe Equation ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Rsos Models ◽  
Bethe Equations ◽  
The Relationship

We outline the relationship between the thermodynamic densities and quasiparticle descriptions of spectra of RSOS models with an underlying Bethe equation. We use this to prove completeness of states in some cases and then give an algorithm for the construction of branching functions of their emergent conformal field theories. Starting from the Bethe equations of Dn type, we discuss some aspects of the Zn lattice models.

scholarly journals On the correspondence between boundary and bulk lattice models and (logarithmic) conformal field theories

2017 ◽  
Vol 50 (48) ◽  
pp. 484002 ◽  
Author(s):  
J Belletête ◽  
A M Gainutdinov ◽  
J L Jacobsen ◽  
H Saleur ◽  
R Vasseur
Keyword(s):  
Lattice Models ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field

CONFORMAL FIELD THEORIES COUPLED TO 2-D GRAVITY IN THE CONFORMAL GAUGE

1988 ◽  
Vol 03 (17) ◽  
pp. 1651-1656 ◽  
Author(s):  
F. DAVID
Keyword(s):  
Lattice Models ◽  
Field Theories ◽  
Exact Results ◽  
Conformal Field Theories ◽  
Random Lattice ◽  
Conformal Field ◽  
Conformal Fields ◽  
Arbitrary Genus ◽  
Conformal Gauge

The coupling of conformal field theories to 2-d gravity may be studied in the conformal gauge. As an application, the results of Knizhnik, Polyakov and Zamolodchikov for the scaling dimensions of conformal fields are derived in a simple way. Their conjecture for the susceptibility exponent γ of strings is proven and extended to arbitrary genus surfaces. The result agrees with exact results from random lattice models.

scholarly journals Branes and integrable lattice models

2017 ◽  
Vol 32 (03) ◽  
pp. 1730003 ◽  
Author(s):  
Junya Yagi
Keyword(s):  
Lattice Models ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Two Dimensional ◽  
Supersymmetric Field Theories ◽  
Topological Quantum ◽  
Integrable Lattice ◽  
Integrable Lattice Models ◽  
Topological Quantum Field Theories

This is a brief review of my work on the correspondence between four-dimensional [Formula: see text] supersymmetric field theories realized by brane tilings and two-dimensional integrable lattice models. I explain how to construct integrable lattice models from extended operators in partially topological quantum field theories, and elucidate the correspondence as an application of this construction.

Conformal Field Theories with Extended Symmetries

2020 ◽  
pp. 476-517
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Lie Algebras ◽  
Lattice Models ◽  
Field Theories ◽  
Conformal Transformations ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Conformal Field ◽  
Conformal Models

The conformal transformations may be part of a larger group of symmetry. Chapter 13 discusses several of the extensions of conformal field theory, including supersymmetry, Z N transformations and current algebras. It also covers superconformal models, the Neveu–Schwarz and Ramond sectors, irreducible representations and minimal models, additional symmetry, the supersymmetric Landau–Ginzburg theory, parafermion models, the relation to lattice models, Kac–Moody algebras, Virasoro operators, the Sugawara Formula, maximal weights and conformal models as cosets. The appendix provides for the interested reader a self-contained discussion on the Lie algebras, include the dual Coxeter numbers, properties of weight vectors and roots/simple roots.

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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