Open-closed strings: Two-dimensional extended TQFTs and Frobenius algebras
| dc.creator | Lauda, Aaron D. | |
| dc.creator | Pfeiffer, Hendryk | |
| dc.date | 2005-10-31 | |
| dc.date | 2008-01-06 | |
| dc.date.accessioned | 2026-07-07T09:22:35Z | |
| dc.date.available | 2026-07-07T09:22:35Z | |
| dc.description | We study a special sort of 2-dimensional extended Topological Quantum Field Theories (TQFTs) which we call open-closed TQFTs. These are defined on open-closed cobordisms by which we mean smooth compact oriented 2-manifolds with corners that have a particular global structure in order to model the smooth topology of open and closed string worldsheets. We show that the category of open-closed TQFTs is equivalent to the category of knowledgeable Frobenius algebras. A knowledgeable Frobenius algebra (A,C,i,i^*) consists of a symmetric Frobenius algebra A, a commutative Frobenius algebra C, and an algebra homomorphism i:C->A with dual i^*:A->C, subject to some conditions. This result is achieved by providing a generators and relations description of the category of open-closed cobordisms. In order to prove the sufficiency of our relations, we provide a normal form for such cobordisms which is characterized by topological invariants. Starting from an arbitrary such cobordism, we construct a sequence of moves (generalized handle slides and handle cancellations) which transforms the given cobordism into the normal form. Using the generators and relations description of the category of open-closed cobordisms, we show that it is equivalent to the symmetric monoidal category freely generated by a knowledgeable Frobenius algebra. Our formalism is then generalized to the context of open-closed cobordisms with labeled free boundary components, i.e. to open-closed string worldsheets with D-brane labels at their free boundaries. | |
| dc.description | 47 pages; LaTeX2e with xypic and pstricks macros; corrected typos | |
| dc.identifier | https://arxiv.org/abs/math/0510664 | |
| dc.identifier | http://arxiv.org/abs/math/0510664 | |
| dc.identifier | Topology Appl. 155 No. 7 (2008) 623-666 | |
| dc.identifier | doi:10.1016/j.topol.2007.11.005 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/155423 | |
| dc.subject | Algebraic Topology | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Quantum Algebra | |
| dc.subject | 57R56; 57M99; 81T40; 58E05; 19D23; 18D35 | |
| dc.title | Open-closed strings: Two-dimensional extended TQFTs and Frobenius algebras | |
| dc.type | text |