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Higher-level Appell functions, modular transformations, and characters.

Semikhatov, A. and Taormina, A. and Tipunin, I. (2005) 'Higher-level Appell functions, modular transformations, and characters.', Communications in mathematical physics., 255 (2). pp. 469-512.

Abstract

We study modular transformation properties of a class of indefinite theta series involved in characters of infinite-dimensional Lie superalgebras. The level- Appell functions satisfy open quasiperiodicity relations with additive theta-function terms emerging in translating by the period. Generalizing the well-known interpretation of theta functions as sections of line bundles, the function enters the construction of a section of a rank-(+1) bundle . We evaluate modular transformations of the functions and construct the action of an SL(2,) subgroup that leaves the section of constructed from invariant. Modular transformation properties of are applied to the affine Lie superalgebra at a rational level k>–1 and to the N=2 super-Virasoro algebra, to derive modular transformations of admissible characters, which are not periodic under the spectral flow and cannot therefore be rationally expressed through theta functions. This gives an example where constructing a modular group action involves extensions among representations in a nonrational conformal model.

Item Type:Article
Full text:PDF - Accepted Version (576Kb)
Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.1007/s00220-004-1280-7
Publisher statement:The original publication is available at www.springerlink.com
Record Created:26 Feb 2008
Last Modified:16 Apr 2013 10:58

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