Lie algebra automorphism in conformal field theory. (English) Zbl 1020.17019
Berman, Stephen (ed.) et al., Recent developments in infinite-dimensional Lie algebras and conformal field theory. Proceedings of an international conference, Charlottesville, VA, USA, May 23-27, 2000. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 297, 117-142 (2002).
In this paper, which is a survey to a large extent, the authors examine the role of automorphisms of infinite-dimensional Lie algebras in conformal field theory, and they discuss two types of applications, related to the enhancement of symmetries and the restriction of observables respectively. The structures one encounters appear in various physical contexts. The ones discussed in the paper are the sub-bundle structure of chiral blocks (where the encountered structures lead to two conjectures) and symmetry reduction caused by the presence of boundaries (where the encountered structures are instrumental).
For the entire collection see [Zbl 0994.00024].
For the entire collection see [Zbl 0994.00024].
Reviewer: Volodymyr Mazorchuk (Uppsala)
MSC:
| 17B69 | Vertex operators; vertex operator algebras and related structures |
| 81R10 | Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations |
| 14H60 | Vector bundles on curves and their moduli |
| 17B81 | Applications of Lie (super)algebras to physics, etc. |
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
