2014/07/06 by Dražen Adamović, Drazen Adamovic, Adamovic, Drazen · 2 citations
Mathematics · Physics and Astronomy · #17B67 #17B68 #17B69 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT) #hep-th #math-ph #math.MP #math.QA #math.RT #msc:17B67 #msc:17B68 #msc:17B69
paper · pdf · doi:10.48550/arxiv.1407.1527
27 pages
arxiv created 2014/07/06 · openalex publication_date 2014/07/06 · arxiv updated 2014/07/08 · openalex created_date 2022/09/14 · openalex updated_date 2026/07/28
We shall first present an explicit realization of the simple N=4 superconformal vertex algebra Lc N=4 with central charge c=-9. This vertex superalgebra is realized inside of the b c βγ system and contains a subalgebra isomorphic to the simple affine vertex algebra LA1 (- \tfrac32 Λ0). Then we construct a functor from the category of Lc N=4--modules with c=-9 to the category of modules for the admissible affine vertex algebra L_A2 (-\tfrac32 Λ0). By using this construction we construct a family of weight and logarithmic modules for Lc N=4 and L_A2 (-\tfrac32 Λ0). We also show that a coset subalgebra of L_A2 (-\tfrac32 Λ0) 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 LA1 (k Λ0) such that k+2 = 1/p and p is a positive integer.