Quantum group symmetry for the Φ12-perturbed and Φ21-perturbed minimal models of conformal field theory

1993 ◽  
Vol 398 (3) ◽  
pp. 697-740 ◽  
Author(s):  
Costas J. Efthimiou
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Quantum Group ◽  
Group Symmetry ◽  
Minimal Models ◽  
Conformal Field

A comment on quantum group symmetry in conformal field theory

1989 ◽  
Vol 328 (3) ◽  
pp. 557-574 ◽  
Author(s):  
Gregory Moore ◽  
Nicolai Reshetikhin
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Quantum Group ◽  
Group Symmetry ◽  
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.

POISSON–LIE GROUPS AND CLASSICAL W-ALGEBRAS

1992 ◽  
Vol 07 (05) ◽  
pp. 853-876 ◽  
Author(s):  
V. A. FATEEV ◽  
S. L. LUKYANOV
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Quantum Group ◽  
Lie Groups ◽  
Group Structure ◽  
Two Dimensional ◽  
Poisson Structures ◽  
Additional Symmetries ◽  
Conformal Field ◽  
Poisson Lie Groups

This is the first part of a paper studying the quantum group structure of two-dimensional conformal field theory with additional symmetries. We discuss the properties of the Poisson structures possessing classical W-invariance. The Darboux variables for these Poisson structures are constructed.

scholarly journals Minimal lectures on two-dimensional conformal field theory

2018 ◽  
Author(s):  
Sylvain Ribault
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Conformal Invariance ◽  
Existence And Uniqueness ◽  
Riemann Sphere ◽  
Liouville Theory ◽  
Two Dimensional ◽  
Minimal Models ◽  
Ward Identities ◽  
Conformal Field

We provide a brief but self-contained review of conformal field theory on the Riemann sphere. We first introduce general axioms such as local conformal invariance, and derive Ward identities and BPZ equations. We then define minimal models and Liouville theory by specific axioms on their spectrums and degenerate fields. We solve these theories by computing three- and four-point functions, and discuss their existence and uniqueness.

scholarly journals NUMBER THEORETIC PROPERTIES OF WRONSKIANS OF ANDREWS–GORDON SERIES

2008 ◽  
Vol 04 (02) ◽  
pp. 323-337 ◽  
Author(s):  
ANTUN MILAS ◽  
ERIC MORTENSON ◽  
KEN ONO
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Positive Integer ◽  
Minimal Models ◽  
Characteristic P ◽  
Partition Identities ◽  
Arithmetic Properties ◽  
Conformal Field ◽  
Supersingular Elliptic Curves ◽  
Positive Integers

For positive integers 1 ≤ i ≤ k, we consider the arithmetic properties of quotients of Wronskians in certain normalizations of the Andrews–Gordon q-series [Formula: see text] This study is motivated by their appearance in conformal field theory, where these series are essentially the irreducible characters of [Formula: see text] Virasoro minimal models. We determine the vanishing of such Wronskians, a result whose proof reveals many partition identities. For example, if Pb(a;n) denotes the number of partitions of n into parts which are not congruent to 0, ±a ( mod b), then for every positive integer n, we have [Formula: see text] We also show that these quotients classify supersingular elliptic curves in characteristic p. More precisely, if 2k + 1 = p, where p ≥ 5 is prime, and the quotient is non-zero, then it is essentially the locus of supersingular j-invariants in characteristic p.

scholarly journals MASSIVE-CONFORMAL DICTIONARY

1994 ◽  
Vol 09 (32) ◽  
pp. 5753-5767 ◽  
Author(s):  
EZER MELZER
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Bethe Ansatz ◽  
Finite Volume ◽  
Energy Levels ◽  
Infinite Volume ◽  
Minimal Models ◽  
Combinatorial Interpretation ◽  
Conformal Field ◽  
Quantum Numbers

The finite-volume spectrum of an integrable massive perturbation of a rational conformal field theory interpolates between massive multiparticle states in infinite-volume (IR limit) and conformal states, which are approached at zero volume (UV limit). Each state is labeled in the IR by a set of “Bethe-ansatz quantum numbers,” while in the UV limit it is characterized primarily by the conformal dimensions of the conformal field creating it. We present explicit conjectures for the UV conformal dimensions corresponding to any IR state in the ϕ1, 3-perturbed minimal models ℳ(2, 5) and ℳ(3, 5). The conjectures, which are based on a combinatorial interpretation of the Rogers-Ramanujan-Schur identities, are consistent with numerical results obtained previously for low-lying energy levels.

scholarly journals On the Real Part of a Conformal Field Theory

Universe ◽  
2018 ◽  
Vol 4 (9) ◽  
pp. 97
Author(s):  
Doron Gepner ◽  
Hervé Partouche
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Coulomb Gas ◽  
Field Theories ◽  
Partition Functions ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Conformal Field ◽  
Exceptional Holonomy ◽  
General Method

Every conformal field theory has the symmetry of taking each field to its adjoint. We consider here the quotient (orbifold) conformal field theory obtained by twisting with respect to this symmetry. A general method for computing such quotients is developed using the Coulomb gas representation. Examples of parafermions, S U ( 2 ) current algebra and the N = 2 minimal models are described explicitly. The partition functions and the dimensions of the disordered fields are given. This result is a tool for finding new theories. For instance, it is of importance in analyzing the conformal field theories of exceptional holonomy manifolds.

scholarly journals JORDAN CELLS IN LOGARITHMIC LIMITS OF CONFORMAL FIELD THEORY

2007 ◽  
Vol 22 (01) ◽  
pp. 67-82 ◽  
Author(s):  
JØRGEN RASMUSSEN
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Field Theories ◽  
General Construction ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Conformal Field ◽  
Arbitrary Rank ◽  
Jordan Cells ◽  
Virasoro Characters

It is discussed how a limiting procedure of conformal field theories may result in logarithmic conformal field theories with Jordan cells of arbitrary rank. This extends our work on rank-two Jordan cells. We also consider the limits of certain three-point functions and find that they are compatible with known results. The general construction is illustrated by logarithmic limits of minimal models in conformal field theory. Characters of quasirational representations are found to emerge as the limits of the associated irreducible Virasoro characters.

Sign in / Sign up

Export Citation Format

Share Document