scholarly journals A remark about the anomalies of cyclic holomorphic permutation orbifolds

2020 ◽  
Vol 31 (10) ◽  
pp. 2050080
Author(s):  
M. Bischoff
Keyword(s):  
Central Charge ◽  
Cyclic Permutation ◽  
Gravitational Anomaly ◽  
Anomaly Formula ◽  
Charge Formula

Using a result of Longo and Xu, we show that the anomaly arising from a cyclic permutation orbifold of order 3 of a holomorphic conformal net [Formula: see text] with central charge [Formula: see text] depends on the “gravitational anomaly” [Formula: see text]. In particular, the conjecture that holomorphic permutation orbifolds are non-anomalous and therefore a stronger conjecture of Müger about braided crossed [Formula: see text]-categories arising from permutation orbifolds of completely rational conformal nets are wrong. More generally, we show that cyclic permutations of order [Formula: see text] are non-anomalous if and only if [Formula: see text] or [Formula: see text]. We also show that all cyclic permutation gaugings of [Formula: see text] arise from conformal nets.

SUPERCONFORMAL ORBIFOLDS INVOLVING THE FERMION NUMBER OPERATOR

2004 ◽  
Vol 19 (22) ◽  
pp. 3637-3667 ◽  
Author(s):  
KATRIN WENDLAND
Keyword(s):  
Central Charge ◽  
Space Time ◽  
Field Theories ◽  
Two Dimensional ◽  
Number Operator ◽  
Superconformal Field Theories ◽  
Fermion Number ◽  
Multicritical Points ◽  
Arbitrary Dimensions ◽  
Charge Formula

We consider orbifolds of two-dimensional unitary toroidal superconformal field theories with target spaces of arbitrary dimensions, where the orbifold group involves the space–time fermion number operator. We construct all so-called superaffine, orbifold prime and super-M-orbifold models by generalizing the constructions of Dixon, Ginsparg and Harvey. We also correct claims made by Dixon, Ginsparg and Harvey about multicritical points among those models with central charge [Formula: see text].

scholarly journals Holomorphic integer graded vertex superalgebras

2021 ◽  
Author(s):  
Jethro van Ekeren ◽  
Bely Rodríguez Morales
Keyword(s):  
Central Charge ◽  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Weight One ◽  
Charge Formula

In this paper, we study holomorphic [Formula: see text]-graded vertex superalgebras. We prove that all such vertex superalgebras of central charge [Formula: see text] and [Formula: see text] are purely even. For the case of central charge [Formula: see text] we prove that the weight-one Lie superalgebra is either zero, of superdimension [Formula: see text], or else is one of an explicit list of 1332 semisimple Lie superalgebras.

scholarly journals THE ORBIFOLD-STRING THEORIES OF PERMUTATION-TYPE II: CYCLE DYNAMICS AND TARGET SPACE–TIME DIMENSIONS

2010 ◽  
Vol 25 (30) ◽  
pp. 5487-5515
Author(s):  
M. B. HALPERN
Keyword(s):  
Physical State ◽  
Central Charge ◽  
Space Time ◽  
Target Space ◽  
Twisted Sector ◽  
Time Dimension ◽  
State Problem ◽  
Dimension Formula ◽  
Charge Formula ◽  
String Theories

We continue our discussion of the general bosonic prototype of the new orbifold-string theories of permutation-type. Supplementing the extended physical-state conditions of the previous paper, we construct here the extended Virasoro generators with cycle central charge [Formula: see text], where fj(σ) is the length of cycle j in twisted sector σ. We also find an equivalent, reduced formulation of each physical-state problem at reduced cycle central charge cj(σ) = 26. These tools are used to begin the study of the target space–time dimension [Formula: see text] of cycle j in sector σ, which is naturally defined as the number of zero modes (momenta) of each cycle. The general model-dependent formulae derived here will be used extensively in succeeding papers, but are evaluated in this paper only for the simplest case of the "pure" permutation orbifolds.

ADE SUBALGEBRAS OF THE TRIPLET VERTEX ALGEBRA $\mathcal{W}(p)$: A-SERIES

2013 ◽  
Vol 15 (06) ◽  
pp. 1350028 ◽  
Author(s):  
DRAŽEN ADAMOVIĆ ◽  
XIANZU LIN ◽  
ANTUN MILAS
Keyword(s):  
Central Charge ◽  
Strong Support ◽  
Vertex Algebra ◽  
Finite Subgroup ◽  
Irreducible Representations ◽  
Finite Subgroups ◽  
Complete Set ◽  
Ade Classification ◽  
Charge Formula

Motivated by [On the triplet vertex algebra [Formula: see text], Adv. Math.217 (2008) 2664–2699], for every finite subgroup Γ ⊂ PSL(2, ℂ) we investigate the fixed point subalgebra [Formula: see text] of the triplet vertex [Formula: see text], of central charge [Formula: see text], p ≥ 2. This part deals with the A-series in the ADE classification of finite subgroups of PSL(2, ℂ). First, we prove the C2-cofiniteness of the Am-fixed subalgebra [Formula: see text]. Then we construct a family of [Formula: see text]-modules, which are expected to form a complete set of irreducible representations. As a strong support to our conjecture, we prove modular invariance of (generalized) characters of the relevant (logarithmic) modules. Further evidence is provided by calculations in Zhu's algebra for m = 2. We also present a rigorous proof of the fact that the full automorphism group of [Formula: see text] is PSL(2, ℂ).

On parafermion vertex algebras of 𝔰𝔩(2) and 𝔰𝔩(3) at level −3 2

2020 ◽  
pp. 2050086
Author(s):  
Dražen Adamović ◽  
Antun Milas ◽  
Qing Wang
Keyword(s):  
Lie Algebra ◽  
Central Charge ◽  
Vertex Algebra ◽  
Vertex Algebras ◽  
Algebraic Proof ◽  
Direct Sums ◽  
Direct Sum ◽  
Irreducible Modules ◽  
Level 3 ◽  
Charge Formula

We study parafermion vertex algebras [Formula: see text] and [Formula: see text]. Using the isomorphism between [Formula: see text] and the logarithmic vertex algebra [Formula: see text] from [D. Adamović, A realization of certain modules for the [Formula: see text] superconformal algebra and the affine Lie algebra [Formula: see text], Transform. Groups 21(2) (2016) 299–327], we show that these parafermion vertex algebras are infinite direct sums of irreducible modules for the Zamolodchikov algebra [Formula: see text] of central charge [Formula: see text], and that [Formula: see text] is a direct sum of irreducible [Formula: see text]-modules. As a byproduct, we prove certain conjectures about the vertex algebra [Formula: see text]. We also obtain a vertex-algebraic proof of the irreducibility of a family of [Formula: see text] modules at [Formula: see text].

scholarly journals REPRESENTATIONS OF N=1 EXTENDED SUPERCONFORMAL ALGEBRAS WITH TWO GENERATORS

1993 ◽  
Vol 08 (08) ◽  
pp. 725-738 ◽  
Author(s):  
W. EHOLZER ◽  
A. HONECKER ◽  
R. HÜBEL
Keyword(s):  
Central Charge ◽  
Mixed Structure ◽  
Rational Models ◽  
Highest Weight ◽  
Continuous Branch ◽  
Highest Weight Representations ◽  
Exceptional Algebras ◽  
Discrete Values ◽  
Ade Classification ◽  
Charge Formula

In this paper we consider the representation theory of N=1 Super-W-algebras with two generators for conformal dimension of the additional superprimary field between two and six. In the superminimal case our results coincide with the expectation from the ADE-classification. For the parabolic algebras we find a finite number of highest weight representations and an effective central charge [Formula: see text]. Furthermore we show that most of the exceptional algebras lead to new rational models with [Formula: see text]. The remaining exceptional cases show a new ‘mixed’ structure. Besides a continuous branch of representations discrete values of the highest weight also exist.

scholarly journals Strong gauging or decoupling ghost matter

2015 ◽  
Vol 30 (24) ◽  
pp. 1550155
Author(s):  
Yu Nakayama
Keyword(s):  
Field Theory ◽  
Fixed Point ◽  
Effective Field Theory ◽  
Gauge Theories ◽  
Central Charge ◽  
Effective Field ◽  
Strongly Coupled ◽  
Weakly Coupled ◽  
Simple Deformation ◽  
Charge Formula

Gauging extra matter is a common way to couple two CFTs discontinuously. We may consider gauging matter by strongly coupled gauge theories at criticality rather than by weakly coupled (asymptotic free) gauge theories. It often triggers relevant deformations and possibly leads to a nontrivial fixed point. In many examples such as the IR limit of SQCDs (and their variants), the relevant RG flow induced by this strong gauging makes the total central charge [Formula: see text] increase rather than decrease compared with the sum of the original decoupled CFTs. The dilaton effective field theory argument given by Komargodski and Schwimmer does not apply because strong gauging is not a simple deformation by operators in the original two decoupled CFTs and it may not be UV complete. When the added matter is vector-like, one may emulate strong gauging in a UV completed manner by decoupling of ghost matter. While the UV completed description makes the dilaton effective field theory argument possible, due to the nonunitarity, we cannot conclude the positivity of the central charge difference in accordance with the observations in various examples that show the contrary.

scholarly journals Free partition functions and an averaged holographic duality

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nima Afkhami-Jeddi ◽  
Henry Cohn ◽  
Thomas Hartman ◽  
Amirhossein Tajdini
Keyword(s):  
Partition Function ◽  
Spectral Gap ◽  
Central Charge ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Partition Functions ◽  
General Constraints ◽  
Dimensional Gravity ◽  
Holographic Duality

Abstract We study the torus partition functions of free bosonic CFTs in two dimensions. Integrating over Narain moduli defines an ensemble-averaged free CFT. We calculate the averaged partition function and show that it can be reinterpreted as a sum over topologies in three dimensions. This result leads us to conjecture that an averaged free CFT in two dimensions is holographically dual to an exotic theory of three-dimensional gravity with U(1)c×U(1)c symmetry and a composite boundary graviton. Additionally, for small central charge c, we obtain general constraints on the spectral gap of free CFTs using the spinning modular bootstrap, construct examples of Narain compactifications with a large gap, and find an analytic bootstrap functional corresponding to a single self-dual boson.

scholarly journals Towards the classification of rank-r $$ \mathcal{N} $$ = 2 SCFTs. Part I. Twisted partition function and central charge formulae

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Mario Martone
Keyword(s):  
Partition Function ◽  
Central Charge ◽  
Singular Locus ◽  
Companion Paper ◽  
Coulomb Branch ◽  
Energy Limit ◽  
Superconformal Field Theories ◽  
Rank 2 ◽  
Explicit Formulae

Abstract We derive explicit formulae to compute the a and c central charges of four dimensional $$ \mathcal{N} $$ N = 2 superconformal field theories (SCFTs) directly from Coulomb branch related quantities. The formulae apply at arbitrary rank. We also discover general properties of the low-energy limit behavior of the flavor symmetry of $$ \mathcal{N} $$ N = 2 SCFTs which culminate with our $$ \mathcal{N} $$ N = 2 UV-IR simple flavor condition. This is done by determining precisely the relation between the integrand of the partition function of the topologically twisted version of the 4d $$ \mathcal{N} $$ N = 2 SCFTs and the singular locus of their Coulomb branches. The techniques developed here are extensively applied to many rank-2 SCFTs, including new ones, in a companion paper.This manuscript is dedicated to the memory of Rayshard Brooks, George Floyd, Breonna Taylor and the countless black lives taken by US police forces and still awaiting justice. Our hearts are with our colleagues of color who suffer daily the consequences of this racist world.

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.

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