NEW SUPERCONFORMAL CONSTRUCTIONS ON TRIANGLE-FREE GRAPHS

1992 ◽  
Vol 07 (29) ◽  
pp. 7263-7286 ◽  
Author(s):  
M.B. HALPERN ◽  
N.A. OBERS
Keyword(s):  
Graph Theory ◽  
Master Equation ◽  
Central Charge ◽  
Field Theories ◽  
Generic Level ◽  
Superconformal Field Theories ◽  
Regular Triangle ◽  
Coset Construction ◽  
Generic Construction ◽  
Almost All

It is known that the superconformal master equation has an ansatz which contains a graph theory of superconformal constructions. In this paper, we study a subansatz which is consistent and solvable on the set of triangle-free graphs. The resulting super-conformal level-families have rational central charge and the constructions are generically unitary. The level-families are generically new because irrational conformal weights occur in the generic construction, and the central charge of the generic level-family cannot be obtained by coset construction. The standard rational superconformal constructions in the subansatz are a subset of the constructions on edge-regular triangle-free graphs, and we call attention to the nonstandard constructions on these graphs as candidates for new rational superconformal field theories. We also find superconformal quadratic deformations at particular levels on almost all edge-regular triangle-free graphs.

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].

SUPERCONFORMAL CONSTRUCTIONS ON TWO-DIMENSIONAL SIMPLICIAL COMPLEXES

1992 ◽  
Vol 07 (13) ◽  
pp. 3065-3082 ◽  
Author(s):  
M. B. HALPERN ◽  
N. A. OBERS
Keyword(s):  
Master Equation ◽  
Central Charge ◽  
Simplicial Complexes ◽  
Large Set ◽  
Two Dimensional ◽  
Infinite Class ◽  
Generic Construction

The superconformal master equation contains a large set of solvable fermionic constructions which live on an infinite class of 2-dimensional simplicial complexes. All the constructions have rational central charge, and irrational conformal weights are expected in the generic construction.

scholarly journals M5-brane sources, holography, and Argyres-Douglas theories

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Ibrahima Bah ◽  
Federico Bonetti ◽  
Ruben Minasian ◽  
Emily Nardoni
Keyword(s):  
Warped Product ◽  
Central Charge ◽  
Field Theories ◽  
Internal Space ◽  
Flavor Symmetry ◽  
Perfect Agreement ◽  
Strongly Coupled ◽  
Superconformal Field Theories ◽  
Holographic Duals ◽  
M Theory

Abstract We initiate a study of the holographic duals of a class of four-dimensional $$ \mathcal{N} $$ N = 2 superconformal field theories that are engineered by wrapping M5-branes on a sphere with an irregular puncture. These notably include the strongly-coupled field theories of Argyres-Douglas type. Our solutions are obtained in 7d gauged supergravity, where they take the form of a warped product of AdS5 and a “half-spindle.” The irregular puncture is modeled by a localized M5-brane source in the internal space of the gravity duals. Our solutions feature a realization of supersymmetry that is distinct from the usual topological twist, as well as an interesting Stückelberg mechanism involving the gauge field associated to a generator of the isometry algebra of the internal space. We check the proposed duality by computing the holographic central charge, the flavor symmetry central charge, and the dimensions of various supersymmetric probe M2-branes, and matching these with the dual Argyres-Douglas field theories. Furthermore, we compute the large-N ’t Hooft anomalies of the field theories using anomaly inflow methods in M-theory, and find perfect agreement with the proposed duality.

NON-UNITARY SUPERSYMMETRIC CONFORMAL FIELD THEORIES AND SUPERSYMMETRIC SINE-GORDON EQUATION

1990 ◽  
Vol 05 (25) ◽  
pp. 2071-2077 ◽  
Author(s):  
SOONKEON NAM
Keyword(s):  
Gordon Equation ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Sine Gordon Equation ◽  
Moody Algebra ◽  
Superconformal Field Theories ◽  
Conformal Field ◽  
The Family ◽  
Coset Construction

We study coset construction of superconformal minimal models using admissible representations of Kac-Moody algebra. In particular, we study supersymmetric minimal models of Wn algebra, and in particular we argue that c = −5/2 cannot be considered as a minimal model of superconformal or super-W3 algebra. In the second part of the paper, we consider superconformal field theories whose perturbations correspond to breather-breather scattering in supersymmetric sine-Gordon equations, and find a family of theories with c = −3N(4N + 3)/2(N + 1), N = 1, 2, 3, …, which is the counterpart of the family of non-unitary theories with c = −2N(6N + 5)/(2N + 3), N = 1, 2, 3, …, among which N = 1 (c = −22/5) is the Yang-Lee edge singularity.

scholarly journals SUPER WEYL ANOMALIES IN THE AdS/CFT CORRESPONDENCE

1999 ◽  
Vol 14 (23) ◽  
pp. 3731-3743 ◽  
Author(s):  
MADOKA NISHIMURA ◽  
YOSHIAKI TANII
Keyword(s):  
Central Charge ◽  
Two Dimensions ◽  
Field Theories ◽  
Conformal Supergravity ◽  
Superconformal Field Theories ◽  
Axial Gauge ◽  
Vector Gauge

Anomalies of N=(4,4) superconformal field theories coupled to a conformal supergravity background in two dimensions are computed by using the AdS/CFT correspondence. We find that Weyl, axial gauge and super Weyl transformations are anomalous, while general coordinate, local Lorentz, vector gauge and local supertransformations are not. The coefficients of the anomalies show that the superconformal field theories have the central charge expected in the AdS/CFT correspondence.

scholarly journals THE SUPERCONFORMAL MASTER EQUATION

1992 ◽  
Vol 07 (05) ◽  
pp. 947-972 ◽  
Author(s):  
A. GIVEON ◽  
M. B. HALPERN ◽  
E. B. KIRITSIS ◽  
N. A. OBERS
Keyword(s):  
Master Equation ◽  
Large Class ◽  
Field Theories ◽  
Signed Graphs ◽  
Superconformal Field Theories ◽  
Superconformal Symmetry ◽  
High Level

We obtain the superconformal master equation, which collects the superconformal solutions of the Virasoro master equation on gx × SO (p, q)1. The associated super C-function and super C-theorem are also obtained. A high-level expansion of the superconformal ansatz { SO (n) diag × SO [ dim SO (n)]1}N=1 shows a large class of new, generically irrational superconformal field theories with a three-form living on the signed graphs of order n. The extension to general N = 2 superconformal symmetry is also given.

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.

BOSONIC CONSTRUCTION OF CONFORMAL FIELD THEORIES WITH EXTENDED SUPERSYMMETRY

1989 ◽  
Vol 04 (03) ◽  
pp. 235-242 ◽  
Author(s):  
YOICHI KAZAMA ◽  
HISAO SUZUKI
Keyword(s):  
Extended Supersymmetry ◽  
Infinite Number ◽  
Central Charge ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Coset Space ◽  
Superconformal Field Theories ◽  
Conformal Field ◽  
Space Method ◽  
Bosonic Representation

A large class of unitary N = 2 superconformal field theories are constructed in the bosonic representation. In particular, they include an infinite number of models with the Virasoro central charge (c) equaling 9, which are generalizations of the ones recently obtained by a coset space method. Similar results are also obtained for c = 6, for which the algebra extends to that with N = 4 supersymmetry.

N=2 SUPERCONFORMAL MODELS AS TOPOLOGICAL FIELD THEORIES

1990 ◽  
Vol 05 (21) ◽  
pp. 1693-1701 ◽  
Author(s):  
TOHRU EGUCHI ◽  
SUNG-KIL YANG
Keyword(s):  
Energy Momentum Tensor ◽  
Central Charge ◽  
Momentum Tensor ◽  
Topological Quantum Field Theory ◽  
Field Theories ◽  
Quantum Field ◽  
Superconformal Field Theories ◽  
Topological Quantum ◽  
Topological Field ◽  
Coset Models

We present simple observations on the topological nature of N=2 superconformal field theories. We point out that under a suitable redefinition of the energy-momentum tensor the central charge of N=2 theory vanishes and the theory is transformed into a topological quantum field theory. BRST invariant observables are given by chiral primary fields. We also discuss the relevant perturbations of N=2 and SU(2) coset models.

THE N = 2 SUPERCONFORMAL ℤ3 ORBIFOLD-PRIME MODEL WITH c = 3

2003 ◽  
Vol 18 (07) ◽  
pp. 503-513 ◽  
Author(s):  
SAYIPJAMAL DULAT
Keyword(s):  
Partition Function ◽  
Central Charge ◽  
Field Theories ◽  
Prime Model ◽  
Two Dimensional ◽  
Dimensional Torus ◽  
Modular Invariant ◽  
Superconformal Field Theories

We consider N = 2 superconformal field theories on a two-dimensional torus with central charge c = 3. In particular, we present the partition function for this theory. Furthermore, to generate new theories, we recall general orbifold prescription. Finally, we construct the modular invariant ℤ3 orbifold-prime model.

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