Branes and Quantization

By Sergei Gukov, E. Witten. 2008

154 citations recorded by the source corpus.

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 (B_(cc), B) strings, where B_(cc) and B are two A-branes; B is an ordinary Lagrangian A-brane, and Bcc is a space-filling coisotropic A-brane. B is supported on M, and the choice of ω is encoded in the choice of B_(cc). As an example, we describe from this point of view the representations of the group SL(2,R). Another application is to Chern–Simons gauge theory.

Subfields: Geometry and Topology, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/daeed72b8566d17b6aa749d77ad0db10315ca712

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Sergei Gukov
2. Tudor Dimofte
3. D. Gaiotto
4. E. Witten
5. N. Nekrasov
6. C. Vafa
7. Mathew Bullimore
8. Abhijit Gadde

In Mathematical Physics

1. Sergei Gukov
2. Tudor Dimofte
3. D. Gaiotto
4. E. Witten
5. N. Nekrasov
6. C. Vafa
7. Yuji Tachikawa
8. Mathew Bullimore

In Nuclear and High Energy Physics

1. E. Witten
2. Sergei Gukov
3. Tudor Dimofte
4. D. Gaiotto
5. Tom Mertens
6. G. Turiaci
7. Mathew Bullimore
8. N. Nekrasov

Citations in the corpus

• Quantum Riemann Surfaces in Chern-Simons Theory (2011, background): “More interestingly, holomorphic quantization of the algebra of operators has a natural interpretation in terms of brane quantization [39, 40].”
• The omega deformation, branes, integrability and Liouville theory (2010, methodology): “The construction also has an analog [14] that is similarly related to SU(2) Chern-Simons gauge theory in 2+1 dimensions.”
• Knot Invariants from Four-Dimensional Gauge Theory (2011, background): “The following discussion assumes familiarity with the framework of [70].”
• Solving the Schwarzian via the conformal bootstrap (2017, methodology): “This is the main feature that will allow us later to compute correlation functions since it can be used to turn a correlation function between ZZ-branes (9)This approach to the geometric quantization of the Virasoro group seems related to the one put forward in [35] for compact groups, but using a t”
• Chern-Simons theory and S-duality (2011, background): “1) and the exchange of the gauge group G with the dual group LG suggests that this hidden symmetry should have a physical explanation in the construction of Chern-Simons Hilbert spaces and wavefunctions in terms of four-dimensional N = 4 super-Yang-Mills theory [3, 12, 13] or, equivalently, in terms”
• The Coulomb Branch of 3d N = 4 Theories (2015, background): “Another example of quantization of an operator algebra appeared in [29, 30].”
• A new look at the path integral of quantum mechanics (2010, unknown): “Finally, we make a few remarks about this example that are more fully explained in [9] and are not really needed for the present paper.”
• Analytic Continuation Of Chern-Simons Theory (2010, background): “34) where h is a constant(6) that has been computed in different ways [48, 50].”
• 3-Manifolds and 3d Indices (2011, unknown): “[28,76].”