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## A realization of certain modules for the N=4 superconformal algebra and the affine Lie algebra A_2 ^(1)

A realization of certain modules for the N=4 superconformal algebra and the affine Lie algebra A_2 ^(1) // Transformation groups, 21 (2016), 2; 299-327 doi:10.1007/s00031-015-9349-2 (međunarodna recenzija, članak, znanstveni)

Naslov
A realization of certain modules for the N=4 superconformal algebra and the affine Lie algebra A_2 ^(1)
(A realization of certain modules for the N=4 superconformal algebra and the affine Lie algebra A_2 ^{; ; ; (1)}; ; ;)

Autori

Izvornik
Transformation groups (1083-4362) 21 (2016), 2; 299-327

Ključne riječi
Vertex superalgebras ; affine Lie algebras ; admissible representations ; N = 4 superconformal algebra ; logarithmic CFT

Sažetak
We shall first present an explicit realization of the simple $N=4$ superconformal vertex algebra $L_{; ; ; c}; ; ; ^{; ; ; N=4}; ; ;$ with central charge $c=-9$. This vertex superalgebra is realized inside of the $b c \beta \gamma$ system and contains a subalgebra isomorphic to the simple affine vertex algebra $L_{; ; ; A_1}; ; ; (- \tfrac{; ; ; 3}; ; ; {; ; ; 2}; ; ; \Lambda_0)$. Then we construct a functor from the category of $L_{; ; ; c}; ; ; ^{; ; ; N=4}; ; ;$-- modules with $c=-9$ to the category of modules for the admissible affine vertex algebra $L_{; ; ; A_{; ; ; 2}; ; ; }; ; ; (-\tfrac{; ; ; 3}; ; ; {; ; ; 2}; ; ; \Lambda_0)$. By using this construction we construct a family of weight and logarithmic modules for $L_{; ; ; c}; ; ; ^{; ; ; N=4}; ; ;$ and $L_{; ; ; A_{; ; ; 2}; ; ; }; ; ; (- \tfrac{; ; ; 3}; ; ; {; ; ; 2}; ; ; \Lambda_0)$. We also show that a coset subalgebra of $L_{; ; ; A_{; ; ; 2}; ; ; }; ; ; (- \tfrac{; ; ; 3}; ; ; {; ; ; 2}; ; ; \Lambda_0)$ is an logarithmic extension of the $W(2, 3)$-- algebra with $c=-10$. We discuss some generalizations of our construction based on the extension of affine vertex algebra $L_{; ; ; A_1}; ; ; (k \Lambda_0)$ such that $k+2 = 1/p$ and $p$ is a positive integer.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

Projekt / tema
HRZZ-IP-2013-11-2634 - Algebarske i kombinatorne metode u teoriji verteks algebri (Dražen Adamović, )

Ustanove
Prirodoslovno-matematički fakultet, Matematički odjel, Zagreb

Autor s matičnim brojem:

#### Časopis indeksira:

• Current Contents Connect (CCC)
• Web of Science Core Collection (WoSCC)
• Science Citation Index Expanded (SCI-EXP)
• SCI-EXP, SSCI i/ili A&HCI
• Scopus

#### Uključenost u ostale bibliografske baze podataka:

• MathSciNet
• Zentralblatt fur Mathematik