Higher string functions, higher-level Appell functions, and the logarithmic ^sl(2)_k/u(1) CFT model
| dc.creator | Semikhatov, AM | |
| dc.date | 2007-10-10 | |
| dc.date | 2007-10-15 | |
| dc.date.accessioned | 2026-07-07T12:35:17Z | |
| dc.date.available | 2026-07-07T12:35:17Z | |
| dc.description | We 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.description | 34 pages, amsart++, times. V2: references added; minor changes; some nonsense in B.3.3. corrected | |
| dc.identifier | https://arxiv.org/abs/0710.2028 | |
| dc.identifier | http://arxiv.org/abs/0710.2028 | |
| dc.identifier | Commun.Math.Phys.286:559-592,2009 | |
| dc.identifier | doi:10.1007/s00220-008-0677-0 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/217720 | |
| dc.subject | Quantum Algebra | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Mathematical Physics | |
| dc.subject | Combinatorics | |
| dc.title | Higher string functions, higher-level Appell functions, and the logarithmic ^sl(2)_k/u(1) CFT model | |
| dc.type | text |