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Fusion of symmetric $D$-branes and Verlinde rings | | A.L. Carey
; Bai-Ling Wang
; | | Date: |
15 May 2005 | | Subject: | Mathematical Physics | math-ph hep-th math.MP | | Affiliation: | ANU), Bai-Ling Wang (ANU | | Abstract: | We explain how multiplicative bundle gerbes over a compact, connected and simple Lie group $G$ lead to a certain fusion category of equivariant bundle gerbe modules given by pre-quantizable Hamiltonian $LG$-manifolds arising from Alekseev-Malkin-Meinrenken’s quasi-Hamiltonian $G$-spaces. The motivation comes from string theory namely, by generalising the notion of $D$-branes in $G$ to allow subsets of $G$ that are the image of a $G$-valued moment map we can define a `fusion of $D$-branes’ and a map to the Verlinde ring of the loop group of $G$ which preserves the product structure. The idea is suggested by the theorem of Freed-Hopkins-Teleman. The case where $G$ is not simply connected is studied carefully in terms of equivariant bundle gerbe modules for multiplicative bundle gerbes. | | Source: | arXiv, math-ph/0505040 | | Services: | Forum | Review | PDF | Favorites | |
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