Higher string functions, higher-level Appell functions, and the logarithmic ^sl(2)_k/u(1) CFT model

dc.creatorSemikhatov, AM
dc.date2007-10-10
dc.date2007-10-15
dc.date.accessioned2026-07-07T12:35:17Z
dc.date.available2026-07-07T12:35:17Z
dc.descriptionWe generalize the string functions C_{n,r}(tau) associated with the coset ^sl(2)_k/u(1) to higher string functions A_{n,r}(tau) and B_{n,r}(tau) associated with the coset W(k)/u(1) of the W-algebra of the logarithmically extended ^sl(2)_k conformal field model with positive integer k. The higher string functions occur in decomposing W(k) characters with respect to level-k theta and Appell functions and their derivatives (the characters are neither quasiperiodic nor holomorphic, and therefore cannot decompose with respect to only theta-functions). The decomposition coefficients, to be considered ``logarithmic parafermionic characters,'' are given by A_{n,r}(tau), B_{n,r}(tau), C_{n,r}(tau), and by the triplet \mathscr{W}(p)-algebra characters of the (p=k+2,1) logarithmic model. We study the properties of A_{n,r} and B_{n,r}, which nontrivially generalize those of the classic string functions C_{n,r}, and evaluate the modular group representation generated from A_{n,r}(tau) and B_{n,r}(tau); its structure inherits some features of modular transformations of the higher-level Appell functions and the associated transcendental function Phi.
dc.description34 pages, amsart++, times. V2: references added; minor changes; some nonsense in B.3.3. corrected
dc.identifierhttps://arxiv.org/abs/0710.2028
dc.identifierhttp://arxiv.org/abs/0710.2028
dc.identifierCommun.Math.Phys.286:559-592,2009
dc.identifierdoi:10.1007/s00220-008-0677-0
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/217720
dc.subjectQuantum Algebra
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subjectCombinatorics
dc.titleHigher string functions, higher-level Appell functions, and the logarithmic ^sl(2)_k/u(1) CFT model
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