Modular transformations and Verlinde formulae for logarithmic (p+,p_)-models

Ridout, David and Wood, Simon ORCID: https://orcid.org/0000-0002-8257-0378 2014. Modular transformations and Verlinde formulae for logarithmic (p+,p_)-models. Nuclear Physics B 880 , pp. 175-202. 10.1016/j.nuclphysb.2014.01.010

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Abstract

The (p+,p−)(p+,p−) singlet algebra is a vertex operator algebra that is strongly generated by a Virasoro field of central charge 1−6(p+−p−)2/p+p−1−6(p+−p−)2/p+p− and a single Virasoro primary field of conformal weight (2p+−1)(2p−−1)(2p+−1)(2p−−1). Here, the modular properties of the characters of the uncountably many simple modules of each singlet algebra are investigated and the results used as the input to a continuous analogue of the Verlinde formula to obtain the “fusion rules” of the singlet modules. The effect of the failure of fusion to be exact in general is studied at the level of Verlinde products and the rules derived are lifted to the (p+,p−)(p+,p−) triplet algebras by regarding these algebras as simple current extensions of their singlet cousins. The result is a relatively effortless derivation of the triplet “fusion rules” that agrees with those previously proposed in the literature.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	Elsevier
ISSN:	0550-3213
Date of First Compliant Deposit:	6 December 2016
Date of Acceptance:	11 January 2014
Last Modified:	05 May 2023 17:05
URI:	https://orca.cardiff.ac.uk/id/eprint/96661

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