D-branes and K-theory in 2D topological field theory
171 citations recorded by the source corpus.
This expository paper describes sewing conditions in two-dimensional open/closed topological field theory. We include a description of the G-equivariant case, where G is a finite group. We determine the category of boundary conditions in the case that the closed string algebra is semisimple. In this case we find that sewing constraints – the most primitive form of worldsheet locality – already imply that D-branes are (G-twisted) vector bundles on spacetime. We comment on extensions to cochain-valued theories and various applications. Finally, we give uniform proofs of all relevant sewing theorems using Morse theory.
View Paper: https://www.semanticscholar.org/paper/d92b58f3016dda037cd9f35e4ff4c8cf07b1b066
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- F. Benini
- Clay Córdova
- D. Gaiotto
- Yuji Tachikawa
- Po-Shen Hsin
- E. Witten
- Sergei Gukov
- Lakshya Bhardwaj
Citations in the corpus
- Hochschild homology of structured algebras (2011, unknown): “Here, we follow the terminology of Moore-Segal [45], amongst others.”
- Spin TQFTs and fermionic phases of matter (2015, background): “This spin-TQFT has also been briefly discussed in [22].”
- On 2-group global symmetries and their anomalies (2018, result): “This framework generalizes the axioms of [32] to include global symmetries and parallels the results for two-dimensional TQFTs in [33].”
- The Mukai pairing, I: a categorical approach (2007, background): “Appropriate references for open-closed 2d topological field theories include Moore-Segal [ 14 ], Costello [7] and Lauda-Pfeier [9].”
- On finite symmetries and their gauging in two dimensions (2017, methodology): “This is a generalization of the work by Moore and Segal [10], where two-dimensional TFTs with finite group symmetry were axiomatized.”
- Electric-Magnetic Duality And The Geometric Langlands Program (2006, background): “3, and is part of the usual axioms of open-closed topological field theory [142,143].”