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Coset constructions of logarithmic (1, p) models

Creutzig, Thomas, Ridout, David and Wood, Simon ORCID: 2014. Coset constructions of logarithmic (1, p) models. Letters in Mathematical Physics 104 (5) , pp. 553-583. 10.1007/s11005-014-0680-7

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One of the best understood families of logarithmic onformal field theories consists of the (1, p) models (p = 2, 3, . . .) of central charge c1, p=1 − 6(p − 1)2/p. This family includes the theories corresponding to the singlet algebras M(p) and the triplet algebras W(p), as well as the ubiquitous symplectic fermions theory. In this work, these algebras are realised through a coset construction. The W(2)n algebra of level k was introduced by Feigin and Semikhatov as a (conjectured) quantum hamiltonian reduction of slˆ(n)k, generalising the Bershadsky–Polyakov algebra W(2)3. Inspired by work of Adamović for p = 3, vertex algebras Bp are constructed as subalgebras of the kernel of certain screening charges acting on a rank 2 lattice vertex algebra of indefinite signature. It is shown that for p≤5, the algebra Bp is a quotient of W(2)p−1 at level −(p − 1)2/p and that the known part of the operator product algebra of the latter algebra is consistent with this holding for p> 5 as well. The triplet algebra W(p) is then realised as a coset inside the full kernel of the screening operator, while the singlet algebra M(p) is similarly realised inside Bp. As an application, and to illustrate these results, the coset character decompositions are explicitly worked out for p = 2 and 3.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Publisher: Springer
ISSN: 0377-9017
Last Modified: 02 Nov 2022 09:52

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