Conformal Field Theory and Doplicher-Roberts Reconstruction
| dc.creator | Mueger, Michael | |
| dc.date | 2000-08-21 | |
| dc.date | 2000-11-07 | |
| dc.date.accessioned | 2026-07-07T04:27:57Z | |
| dc.date.available | 2026-07-07T04:27:57Z | |
| dc.description | After a brief review of recent rigorous results concerning the representation theory of rational chiral conformal field theories (RCQFTs) we focus on pairs (A,F) of conformal field theories, where F has a finite group G of global symmetries and A is the fixpoint theory. The comparison of the representation categories of A and F is strongly intertwined with various issues related to braided tensor categories. We explain that, given the representation category of A, the representation category of F can be computed (up to equivalence) by a purely categorical construction. The latter is of considerable independent interest since it amounts to a Galois theory for braided tensor categories. We emphasize the characterization of modular categories as braided tensor categories with trivial center and we state a double commutant theorem for subcategories of modular categories. The latter implies that a modular category M which has a replete full modular subcategory M_1 is equivalent to M_1 x M_2 where M_2=M\cap M_1' is another modular subcategory. On the other hand, the representation category of A is not determined completely by that of F and we identify the needed additional data in terms of soliton representations. We comment on `holomorphic orbifold' theories, i.e. the case where F has trivial representation theory, and close with some open problems. We point out that our approach permits the proof of many conjectures and heuristic results on `simple current extensions' and `holomorphic orbifold models' in the physics literature on conformal field theory. | |
| dc.description | latex, 23 pages, documentclass fic-l, uses diagrams.tex. Final version. Relevance of Turaev's notion of braided crossed G-categories pointed out, otherwise minor changes | |
| dc.identifier | https://arxiv.org/abs/math-ph/0008027 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0008027 | |
| dc.identifier | Fields Inst. Commun. 30, 297-319 (2001) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/56611 | |
| dc.subject | Mathematical Physics | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | 81T40 (Primary), 81T05, 46L60, 18D10 (Secondary) | |
| dc.title | Conformal Field Theory and Doplicher-Roberts Reconstruction | |
| dc.type | text |