Branes and quantization

Sergei Gukov, Edward Witten

Research output: Contribution to journalArticlepeer-review

67 Scopus citations


The problem of quantizing a symplectic manifold (M,ω) can be formulated in terms of the A-model of a complexification of M. This leads to an interesting new perspective on quantization. From this point of view, the Hilbert space obtained by quantization of (M,ω) is the space of (Bcc, B1) strings, where Bcc and B1 are two A-branes; B1 is an ordinary Lagrangian A-brane, and Bcc is a space-filling coisotropic A-brane. B1 is supported on M, and the choice of ω is encoded in the choice of Bcc. As an example, we describe from this point of view the representations of the group SL(2, R{double-struck}). Another application is to Chern-Simons gauge theory.

Original languageEnglish (US)
Pages (from-to)1445-1518
Number of pages74
JournalAdvances in Theoretical and Mathematical Physics
Issue number5
StatePublished - Oct 2009
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • General Physics and Astronomy


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