NOVEL TOPOLOGICAL CONFORMAL ALGEBRAS

1991 ◽  
Vol 06 (14) ◽  
pp. 1321-1332 ◽  
Author(s):  
YOICHI KAZAMA
Keyword(s):  
Central Charge ◽  
The Other ◽  
Field Theories ◽  
Algebraic Characterization ◽  
Conformal Field Theories ◽  
Superconformal Symmetry ◽  
Conformal Field ◽  
Conformal Algebras ◽  
Slight Deformation

Algebraic characterization of 2-dimensional topological conformal field theories (TCFT’s) is proposed and some of its consequences are studied. In particular, we find two kinds of novel closed algebras, both of which are non-trivial extensions of the twisted version of the N=2 superconformal algebra. The larger of these algebras generically allows non-vanishing central charge c, a simple example of which is provided by a system with c=−2. The other algebra, on the other hand, requires vanishing central charge. An intriguing feature of this algebra is that it can be “untwisted” to yield a slight deformation of the N=2 algebra, which nevertheless possesses a hidden N=1 superconformal symmetry.

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 On 2d CFTs that interpolate between minimal models

2019 ◽  
Vol 6 (6) ◽  
Author(s):  
Sylvain Ribault
Keyword(s):  
Correlation Functions ◽  
Central Charge ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Conformal Blocks ◽  
Conformal Field ◽  
Exactly Solvable ◽  
Structure Constants

We investigate exactly solvable two-dimensional conformal field theories that exist at generic values of the central charge, and that interpolate between A-series or D-series minimal models. When the central charge becomes rational, correlation functions of these CFTs may tend to correlation functions of minimal models, or diverge, or have finite limits which can be logarithmic. These results are based on analytic relations between four-point structure constants and residues of conformal blocks.

scholarly journals THE CAPPELLI–ITZYKSON–ZUBER A-D-E CLASSIFICATION

2000 ◽  
Vol 12 (05) ◽  
pp. 739-748 ◽  
Author(s):  
TERRY GANNON
Keyword(s):  
Mathematical Structure ◽  
The Other ◽  
Field Theories ◽  
Partition Functions ◽  
Conformal Field Theories ◽  
Modular Invariant ◽  
Conformal Field ◽  
Affine Algebras ◽  
Order Of Magnitude ◽  
The Rich

In 1986 Cappelli, Itzykson and Zuber classified all modular invariant partition functions for the conformal field theories associated to the affine A1 algebra; they found they fall into an A-D-E pattern. Their proof was difficult and attempts to generalise it to the other affine algebras failed — in hindsight the reason is that their argument ignored most of the rich mathematical structure present. We give here the "modern" proof of their result; it is an order of magnitude simpler and shorter, and much of it has already been extended to all other affine algebras. We conclude with some remarks on the A-D-E pattern appearing in this and other RCFT classifications.

scholarly journals FUSION ALGEBRAS INDUCED BY REPRESENTATIONS OF THE MODULAR GROUP

1993 ◽  
Vol 08 (20) ◽  
pp. 3495-3507 ◽  
Author(s):  
W. EHOLZER
Keyword(s):  
Representation Theory ◽  
Modular Group ◽  
Central Charge ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Rational Models ◽  
Conformal Field

Using the representation theory of the subgroups SL 2(ℤp) of the modular group we investigate the induced fusion algebras in some simple examples. Only some of these representations lead to "good" fusion algebras. Furthermore, the conformal dimensions and the central charge of the corresponding rational conformal field theories are calculated. Two series of representations which can be realized by unitary theories are presented. We show that most of the fusion algebras induced by admissible representations are realized in well-known rational models.

scholarly journals Quantum null energy condition and its (non)saturation in 2d CFTs

2019 ◽  
Vol 6 (3) ◽  
Author(s):  
Christian Ecker ◽  
Daniel Grumiller ◽  
Wilke van der Schee ◽  
Shahin Sheikh-Jabbari ◽  
Philipp Stanzer
Keyword(s):  
Central Charge ◽  
Energy Condition ◽  
Null Energy Condition ◽  
Einstein Gravity ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Leading Order ◽  
Conformal Field ◽  
Primary Operator ◽  
Vacuum Solutions

We consider the Quantum Null Energy Condition (QNEC) for holographic conformal field theories in two spacetime dimensions (CFT_22). We show that QNEC saturates for all states dual to vacuum solutions of AdS_33 Einstein gravity, including systems that are far from thermal equilibrium. If the Ryu-Takayanagi surface encounters bulk matter QNEC does not need to be saturated, whereby we give both analytical and numerical examples. In particular, for CFT_22 with a global quench dual to AdS_33-Vaidya geometries we find a curious half-saturation of QNEC for large entangling regions. We also address order one corrections from quantum backreactions of a scalar field in AdS_33 dual to a primary operator of dimension h in a large central charge expansion and explicitly compute both, the backreacted Ryu–Takayanagi surface part and the bulk entanglement contribution to EE and QNEC. At leading order for small entangling regions the contribution from bulk EE exactly cancels the contribution from the back-reacted Ryu-Takayanagi surface, but at higher orders in the size of the region the contributions are almost equal while QNEC is not saturated. For a half-space entangling region we find that QNEC is gapped by h/4h/4 in the large h expansion.

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 THE LIE h-INVARIANT CONFORMAL FIELD THEORIES AND THE LIE h-INVARIANT GRAPHS

1992 ◽  
Vol 07 (supp01a) ◽  
pp. 339-375 ◽  
Author(s):  
M. B. HALPERN ◽  
E. B. KIRITSIS ◽  
N. A. OBERS
Keyword(s):  
Graph Theory ◽  
General Theory ◽  
Master Equation ◽  
Lie Group ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field

We use the Virasoro master equation to study the space of Lie h-invariant conformal field theories, which includes the standard rational conformal field theories as a small subspace. In a detailed example, we apply the general theory to characterize and study the Lie h-invariant graphs, which classify the Lie h-invariant conformal field theories of the diagonal ansatz on SO(n). The Lie characterization of these graphs is another aspect of the recently observed Lie group-theoretic structure of graph theory.

PERTURBING INDUCED QUANTUM SUPERGRAVITY IN 1 + 1 DIMENSIONS

1990 ◽  
Vol 05 (11) ◽  
pp. 2087-2115 ◽  
Author(s):  
WAFIC A. SABRA ◽  
STEVEN THOMAS
Keyword(s):  
Correlation Functions ◽  
Scale Invariance ◽  
Central Charge ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Breaking Scale

Starting from the formulation of induced (1, 0) supergravity in 1 + 1 dimensions we consider the effects of perturbing the theory with relevant operators that preserve rotational, translational and supersymmetry whilst breaking scale invariance. In particular we calculate the correlation functions <Ja(x)Jb(y)> of graded SL (2R) currents Ja(x) in the presence of such perturbations from which we define central charge functions K. These functions are shown to be monotonic and are the analogue of Zamolodchikovs C-function as defined in usual conformal field theories.

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