Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), ISSN 1815-0659, 2012, Volume 8, p. 040

We give a coset realization of the vertex operator algebra M(1)(+) with central charge l. We realize M(1...

Coset vertex algebra | W-algebra | Con- formal embedding | Vertex operator algebra | Affine Kac-Moody algebra | vertex operator algebra | REPRESENTATIONS | CLASSIFICATION | RANK | OPERATOR-ALGEBRAS | PHYSICS, MATHEMATICAL | affine Kac-Moody algebra | LIE-ALGEBRAS | VIRASORO ALGEBRAS | IRREDUCIBLE MODULES | W-ALGEBRAS | SUPERALGEBRAS | coset vertex algebra | conformal embedding

Coset vertex algebra | W-algebra | Con- formal embedding | Vertex operator algebra | Affine Kac-Moody algebra | vertex operator algebra | REPRESENTATIONS | CLASSIFICATION | RANK | OPERATOR-ALGEBRAS | PHYSICS, MATHEMATICAL | affine Kac-Moody algebra | LIE-ALGEBRAS | VIRASORO ALGEBRAS | IRREDUCIBLE MODULES | W-ALGEBRAS | SUPERALGEBRAS | coset vertex algebra | conformal embedding

Journal Article

Journal of High Energy Physics, ISSN 1126-6708, 1/2019, Volume 2019, Issue 1, pp. 1 - 88

We introduce a class of Vertex Operator Algebras which arise at junctions of supersymmetric interfaces in N $$ \mathcal{N...

Wilson, ’t Hooft and Polyakov loops | Duality in Gauge Field Theories | Extended Supersymmetry | Quantum Physics | Conformal and W Symmetry | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | t Hooft and Polyakov loops | FIELD-THEORY | Wilson | REPRESENTATION | DUALITY | BRANES | QUANTIZATION | PHYSICS, PARTICLES & FIELDS | Supersymmetry | Gauge theory | Algebra | Dislocations

Wilson, ’t Hooft and Polyakov loops | Duality in Gauge Field Theories | Extended Supersymmetry | Quantum Physics | Conformal and W Symmetry | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | t Hooft and Polyakov loops | FIELD-THEORY | Wilson | REPRESENTATION | DUALITY | BRANES | QUANTIZATION | PHYSICS, PARTICLES & FIELDS | Supersymmetry | Gauge theory | Algebra | Dislocations

Journal Article

3.
Full Text
Conformal embeddings of affine vertex algebras in minimal W-algebras I: Structural results

Journal of Algebra, ISSN 0021-8693, 04/2018, Volume 500, pp. 117 - 152

We find all values of k∈C, for which the embedding of the maximal affine vertex algebra in a simple minimal W-algebra Wk(g,θ...

Vertex algebra | Conformal level | Virasoro (=conformal) vector | Conformal embedding | Collapsing level | MATHEMATICS | DECOMPOSITIONS | REPRESENTATION-THEORY | SPACES | SUPERCONFORMAL ALGEBRAS | SUPERALGEBRAS | Virasoro (= conformal) vector | SUBALGEBRAS | QUANTUM REDUCTION | Mathematics - Representation Theory

Vertex algebra | Conformal level | Virasoro (=conformal) vector | Conformal embedding | Collapsing level | MATHEMATICS | DECOMPOSITIONS | REPRESENTATION-THEORY | SPACES | SUPERCONFORMAL ALGEBRAS | SUPERALGEBRAS | Virasoro (= conformal) vector | SUBALGEBRAS | QUANTUM REDUCTION | Mathematics - Representation Theory

Journal Article

JOURNAL OF HIGH ENERGY PHYSICS, ISSN 1029-8479, 05/2019, Volume 2019, Issue 5, pp. 1 - 39

We introduce two mirror constructions of Vertex Operator Algebras associated to special boundary conditions in 3d N = 4 gauge theories...

Duality in Gauge Field Theories | BOUNDARY-CONDITIONS | Conformal Field Theory | Extended Supersymmetry | TOPOLOGICAL FIELD-THEORY | S-DUALITY | Topological Field Theories | PHYSICS, PARTICLES & FIELDS | Analysis | Algebra | Boundary conditions

Duality in Gauge Field Theories | BOUNDARY-CONDITIONS | Conformal Field Theory | Extended Supersymmetry | TOPOLOGICAL FIELD-THEORY | S-DUALITY | Topological Field Theories | PHYSICS, PARTICLES & FIELDS | Analysis | Algebra | Boundary conditions

Journal Article

Journal of Algebra, ISSN 0021-8693, 03/2020, Volume 546, pp. 689 - 702

Herein we study conformal vectors of a Z-graded vertex algebra of (strong) CFT type. We prove that the full vertex algebra automorphism group transitively acts...

Conformal vectors | Conformal field theory | Vertex operator algebras | The Monster group | Vertex Algebras | MATHEMATICS | MOONSHINE | Mathematics - Quantum Algebra

Conformal vectors | Conformal field theory | Vertex operator algebras | The Monster group | Vertex Algebras | MATHEMATICS | MOONSHINE | Mathematics - Quantum Algebra

Journal Article

Advances in Mathematics, ISSN 0001-8708, 2008, Volume 217, Issue 6, pp. 2664 - 2699

We study the triplet vertex operator algebra W ( p ) of central charge 1 − 6 ( p − 1 ) 2 p , p ⩾ 2 . We show that W ( p ) is C 2 -cofinite but irrational since it admits indecomposable and logarithmic modules...

Vertex algebras | [formula omitted]-algebras | Logarithmic conformal field theory | W-algebras | MATHEMATICS | vertex algebras | FUSION | REPRESENTATIONS | W1+INFINITY | CONFORMAL FIELD-THEORIES | MODULAR-INVARIANCE | OPERATOR-ALGEBRAS | logarithmic conformal field theory | CHARACTERS

Vertex algebras | [formula omitted]-algebras | Logarithmic conformal field theory | W-algebras | MATHEMATICS | vertex algebras | FUSION | REPRESENTATIONS | W1+INFINITY | CONFORMAL FIELD-THEORIES | MODULAR-INVARIANCE | OPERATOR-ALGEBRAS | logarithmic conformal field theory | CHARACTERS

Journal Article

Journal of Algebra, ISSN 0021-8693, 01/2014, Volume 397, pp. 252 - 277

Unitary vertex operator algebras are introduced and studied. It is proved that most well-known rational vertex operator algebras are unitary...

Unitary vertex operator algebras | MATHEMATICS | MODULAR-INVARIANCE | EVEN LATTICES | REPRESENTATIONS | CONFORMAL NETS | Algebra

Unitary vertex operator algebras | MATHEMATICS | MODULAR-INVARIANCE | EVEN LATTICES | REPRESENTATIONS | CONFORMAL NETS | Algebra

Journal Article

Nuclear Physics, Section B, ISSN 0550-3213, 2009, Volume 823, Issue 3, pp. 320 - 371

...) mass, and construct vertex algebra representations of sv out of a charged symplectic boson and a free boson and its associated vertex operators. We also compute two- and three-point functions of still conjectural massive fields that are defined by an analytic continuation with respect to a formal parameter.

Supersymmetry | Schrödinger-invariance | Infinite-dimensional Lie algebras | Non-equilibrium statistical physics | Conformal field-theory | Algebraic structure of integrable models | Correlation functions | Schrodinger-invariance | LOCAL SCALE-INVARIANCE | EQUATIONS | PHASE-ORDERING KINETICS | CONFORMAL-INVARIANCE | SYMMETRY | SYSTEMS | PHYSICS, PARTICLES & FIELDS | Condensed Matter | Statistical Mechanics | Mathematical Physics | Physics

Supersymmetry | Schrödinger-invariance | Infinite-dimensional Lie algebras | Non-equilibrium statistical physics | Conformal field-theory | Algebraic structure of integrable models | Correlation functions | Schrodinger-invariance | LOCAL SCALE-INVARIANCE | EQUATIONS | PHASE-ORDERING KINETICS | CONFORMAL-INVARIANCE | SYMMETRY | SYSTEMS | PHYSICS, PARTICLES & FIELDS | Condensed Matter | Statistical Mechanics | Mathematical Physics | Physics

Journal Article

Journal of High Energy Physics, ISSN 1126-6708, 8/2018, Volume 2018, Issue 8, pp. 1 - 72

Every four-dimensional N=2 $$ \mathcal{N}=2 $$ superconformal field theory comes equipped with an intricate algebraic invariant, the associated vertex operator algebra...

Conformal Field Theory | Extended Supersymmetry | Supersymmetric Gauge Theory | Quantum Physics | Conformal and W Symmetry | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | FORMS | QUIVER VARIETIES | CLASSIFICATION | PHYSICS, PARTICLES & FIELDS | Algebra | Differential equations | Mathematical analysis | Lie groups | Field theory | Vectors (mathematics) | Invariants | Physics - High Energy Physics - Theory | Nuclear and particle physics. Atomic energy. Radioactivity | High Energy Physics - Theory

Conformal Field Theory | Extended Supersymmetry | Supersymmetric Gauge Theory | Quantum Physics | Conformal and W Symmetry | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | FORMS | QUIVER VARIETIES | CLASSIFICATION | PHYSICS, PARTICLES & FIELDS | Algebra | Differential equations | Mathematical analysis | Lie groups | Field theory | Vectors (mathematics) | Invariants | Physics - High Energy Physics - Theory | Nuclear and particle physics. Atomic energy. Radioactivity | High Energy Physics - Theory

Journal Article

Communications in Contemporary Mathematics, ISSN 0219-1997, 05/2020, Volume 22, Issue 3, p. 1950024

... ) at a 2 p th root of unity. The representation category of U is conjecturally ribbon equivalent to that of the triplet vertex operator algebra (VOA) ( p...

CORRELATORS | braided tensor categories | MATHEMATICS, APPLIED | FUSION RULES | EXTENSIONS | INVARIANTS | TFT CONSTRUCTION | quasi-Hopf algebras | CATEGORIES | MATHEMATICS | MODULAR TRANSFORMATIONS | Vertex operator algebras | FALSE THETA-FUNCTIONS | quantum groups | SIMPLE CURRENTS | logarithmic modules | CONFORMAL FIELD-THEORIES | Quantum Algebra | Mathematics | High Energy Physics - Theory | Physics | Representation Theory

CORRELATORS | braided tensor categories | MATHEMATICS, APPLIED | FUSION RULES | EXTENSIONS | INVARIANTS | TFT CONSTRUCTION | quasi-Hopf algebras | CATEGORIES | MATHEMATICS | MODULAR TRANSFORMATIONS | Vertex operator algebras | FALSE THETA-FUNCTIONS | quantum groups | SIMPLE CURRENTS | logarithmic modules | CONFORMAL FIELD-THEORIES | Quantum Algebra | Mathematics | High Energy Physics - Theory | Physics | Representation Theory

Journal Article

Journal of High Energy Physics, ISSN 1126-6708, 12/2017, Volume 2017, Issue 12, pp. 1 - 36

We study aspects of the vertex operator algebra (VOA) corresponding to Argyres-Douglas (AD...

Supersymmetric Gauge Theory | Topological Field Theories | Quantum Physics | Conformal and W Symmetry | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Supersymmetry and Duality | Physics | Elementary Particles, Quantum Field Theory | LIE-ALGEBRAS | GAUGE-THEORIES | DRINFELD-SOKOLOV REDUCTION | SYMMETRY | W-ALGEBRAS | SUPERCONFORMAL FIELD-THEORIES | CHARACTERS | PHYSICS, PARTICLES & FIELDS | Analysis | Algebra | Resveratrol | Deformation | Mathematical analysis | Branes | Mathematics - Quantum Algebra | Nuclear and particle physics. Atomic energy. Radioactivity | High Energy Physics - Theory | Mathematics - Representation Theory | conformal and W symmetry | supersymmetric gauge theory | PHYSICS OF ELEMENTARY PARTICLES AND FIELDS | supersymmetry and duality | topological field theories

Supersymmetric Gauge Theory | Topological Field Theories | Quantum Physics | Conformal and W Symmetry | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Supersymmetry and Duality | Physics | Elementary Particles, Quantum Field Theory | LIE-ALGEBRAS | GAUGE-THEORIES | DRINFELD-SOKOLOV REDUCTION | SYMMETRY | W-ALGEBRAS | SUPERCONFORMAL FIELD-THEORIES | CHARACTERS | PHYSICS, PARTICLES & FIELDS | Analysis | Algebra | Resveratrol | Deformation | Mathematical analysis | Branes | Mathematics - Quantum Algebra | Nuclear and particle physics. Atomic energy. Radioactivity | High Energy Physics - Theory | Mathematics - Representation Theory | conformal and W symmetry | supersymmetric gauge theory | PHYSICS OF ELEMENTARY PARTICLES AND FIELDS | supersymmetry and duality | topological field theories

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 8/2015, Volume 337, Issue 3, pp. 1143 - 1159

Let V be a vertex operator algebra satisfying suitable conditions such that in particular its module category has a natural vertex tensor category structure, and consequently, a natural braided tensor category structure...

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | PRODUCT THEORY | CONFORMAL FIELD-THEORY | PHYSICS, MATHEMATICAL | MODULE CATEGORIES | Algebra

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | PRODUCT THEORY | CONFORMAL FIELD-THEORY | PHYSICS, MATHEMATICAL | MODULE CATEGORIES | Algebra

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 12/2018, Volume 108, Issue 12, pp. 2543 - 2587

The parafermionic cosets $$\mathsf {C}_{k} = {\text {Com}} ( \mathsf {H} , \mathsf {L}_{k}(\mathfrak {sl}_{2}) )$$ Ck=Com(H,Lk(sl2)) are studied for negative...

Geometry | Vertex algebras | Conformal field theory | Parafermions | Theoretical, Mathematical and Computational Physics | Complex Systems | Modular transformations | Secondary 13A50 | Group Theory and Generalizations | Coset constructions | Primary 17B69 | Physics | EXTENDED CONFORMAL ALGEBRAS | FUSION RULES | FIELD-THEORY | OPERATOR-ALGEBRAS | PHYSICS, MATHEMATICAL | CHARACTERS | LIE-ALGEBRAS | INVARIANT REPRESENTATIONS | VERLINDE FORMULAS | CONSTRUCTIONS | C-2-COFINITENESS | Analysis | Algebra

Geometry | Vertex algebras | Conformal field theory | Parafermions | Theoretical, Mathematical and Computational Physics | Complex Systems | Modular transformations | Secondary 13A50 | Group Theory and Generalizations | Coset constructions | Primary 17B69 | Physics | EXTENDED CONFORMAL ALGEBRAS | FUSION RULES | FIELD-THEORY | OPERATOR-ALGEBRAS | PHYSICS, MATHEMATICAL | CHARACTERS | LIE-ALGEBRAS | INVARIANT REPRESENTATIONS | VERLINDE FORMULAS | CONSTRUCTIONS | C-2-COFINITENESS | Analysis | Algebra

Journal Article

Journal of High Energy Physics, ISSN 1126-6708, 3/2019, Volume 2019, Issue 3, pp. 1 - 50

...} $$ = 4 supersymmetric quantum field theories and categories of modules for Vertex Operator Algebras of boundary local operators for the theories...

Conformal Field Theory | Supersymmetric Gauge Theory | Topological Field Theories | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | GAUGE-THEORIES | FALSE THETA-FUNCTIONS | MODELS | VERLINDE FORMULAS | MODULAR DATA | PHYSICS, PARTICLES & FIELDS | Algebra | Supersymmetry | Quantum theory | Dislocations

Conformal Field Theory | Supersymmetric Gauge Theory | Topological Field Theories | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | GAUGE-THEORIES | FALSE THETA-FUNCTIONS | MODELS | VERLINDE FORMULAS | MODULAR DATA | PHYSICS, PARTICLES & FIELDS | Algebra | Supersymmetry | Quantum theory | Dislocations

Journal Article

International Journal of Modern Physics B, ISSN 0217-9792, 11/2016, Volume 30, Issue 28n29, p. 1640030

Starting from Zhu recursion formulas for correlation functions for vertex operator algebras with formal parameters associated to local coordinates around marked points on a Riemann surfaces...

vertex operator algebras | Riemann surfaces | Cluster algebras | PHYSICS, CONDENSED MATTER | PHYSICS, APPLIED | ENSEMBLES | N-POINT FUNCTIONS | MODULAR INVARIANCE | CONFORMAL FIELD-THEORIES | QUANTIZATION | PHYSICS, MATHEMATICAL | DILOGARITHM IDENTITIES | Algebra

vertex operator algebras | Riemann surfaces | Cluster algebras | PHYSICS, CONDENSED MATTER | PHYSICS, APPLIED | ENSEMBLES | N-POINT FUNCTIONS | MODULAR INVARIANCE | CONFORMAL FIELD-THEORIES | QUANTIZATION | PHYSICS, MATHEMATICAL | DILOGARITHM IDENTITIES | Algebra

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 12/2017, Volume 107, Issue 12, pp. 2189 - 2237

This paper focuses on the connection of holomorphic two-dimensional factorization algebras and vertex algebras which has been made precise in the forthcoming book of Costello–Gwilliam...

Geometry | Conformal field theory | 81R10 | Theoretical, Mathematical and Computational Physics | Complex Systems | 17B65 | Group Theory and Generalizations | Virasoro vertex algebra | 18G55 | Physics | Factorization algebras | BV quantization | PHYSICS, MATHEMATICAL | Algebra

Geometry | Conformal field theory | 81R10 | Theoretical, Mathematical and Computational Physics | Complex Systems | 17B65 | Group Theory and Generalizations | Virasoro vertex algebra | 18G55 | Physics | Factorization algebras | BV quantization | PHYSICS, MATHEMATICAL | Algebra

Journal Article

Advances in Mathematics, ISSN 0001-8708, 05/2018, Volume 330, pp. 1160 - 1208

We find a necessary and sufficient condition for the existence of the tensor product of modules over a vertex algebra...

Tensor product | Vertex algebra | MATHEMATICS | CONFORMAL FIELD-THEORY | OPERATOR-ALGEBRAS | CATEGORIES

Tensor product | Vertex algebra | MATHEMATICS | CONFORMAL FIELD-THEORY | OPERATOR-ALGEBRAS | CATEGORIES

Journal Article

Journal of Pure and Applied Algebra, ISSN 0022-4049, 11/2016, Volume 220, Issue 11, pp. 3628 - 3649

We give two constructions of grading-restricted vertex (super)algebras. We first give a new construction of a class of grading-restricted vertex (super...

MATHEMATICS | MATHEMATICS, APPLIED | CONFORMAL FIELD-THEORY | OPERATOR-ALGEBRAS | Algebra

MATHEMATICS | MATHEMATICS, APPLIED | CONFORMAL FIELD-THEORY | OPERATOR-ALGEBRAS | Algebra

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 7/2014, Volume 329, Issue 1, pp. 263 - 294

The mirror extensions for vertex operator algebras are studied. Two explicit examples of extensions of affine vertex operator algebras of type A are given...

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | LOCAL CONFORMAL NETS | TENSOR | REPRESENTATIONS | LEVEL-RANK DUALITY | MATRICES | CLASSIFICATION | AFFINE | MODULAR-INVARIANCE | MODEL | PHYSICS, MATHEMATICAL | VIRASORO | Algebra

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | LOCAL CONFORMAL NETS | TENSOR | REPRESENTATIONS | LEVEL-RANK DUALITY | MATRICES | CLASSIFICATION | AFFINE | MODULAR-INVARIANCE | MODEL | PHYSICS, MATHEMATICAL | VIRASORO | Algebra

Journal Article