Cosets, Characters and Fusion for Admissible-level osp(1|2) Minimal Models
Publication Date
11-3-2018
Document Type
Article
Organizational Units
Mathematics
Keywords
Minimal models, Grothendieck fusion, Highest-weight modules
Abstract
We study the minimal models associated to osp(1|2)" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; display: inline-block; line-height: normal; font-size: 16.2px; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">osp(1|2), otherwise known as the fractional-level Wess–Zumino–Witten models of osp(1|2)" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; display: inline-block; line-height: normal; font-size: 16.2px; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">osp(1|2). Since these minimal models are extensions of the tensor product of certain Virasoro and sl2" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; display: inline-block; line-height: normal; font-size: 16.2px; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">sl2 minimal models, we can induce the known structures of the representations of the latter models to get a rather complete understanding of the minimal models of osp(1|2)" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; display: inline-block; line-height: normal; font-size: 16.2px; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">osp(1|2). In particular, we classify the irreducible relaxed highest-weight modules, determine their characters and compute their Grothendieck fusion rules. We also discuss conjectures for their (genuine) fusion products and the projective covers of the irreducibles.
Publication Statement
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Recommended Citation
Creutzig, Thomas, et al. “Cosets, Characters and Fusion for Admissible-Level Osp(1|2) Minimal Models.” Nuclear Physics. B, vol. 938, 2019, pp. 22–55. doi: 10.1016/j.nuclphysb.2018.10.022.