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Results tagged with mp.mathematical-physics
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user 582
Mathematical methods in classical mechanics, classical and quantum field theory, quantum mechanics, statistical mechanics, condensed matter, nuclear and atomic physics.
19
votes
Accepted
Implications and consequences of the recent proof of the geometric Langlands conjecture
To avoid writing a long essay I'll be very telegraphic.
Here are some of the many open problems that are reasonably "next" in the area. I'll use [GLC] to refer to the recent papers proving the unramif …
- 24.1k
13
votes
Relationship between the TQFTs in Kapustin-Witten and Ben-Zvi-Sakellaridis-Venkatesh
The (fairly poetic and ill-formed) idea in this story is that the Kapustin-Witten story and the Langlands program are about the SAME four-dimensional TQFTs, but evaluated on different "manifolds" - i. …
- 24.1k
5
votes
Path integral derivation of extended TQFT
The original motivation for extended TQFTs (as introduced by Freed, Lawrence, Baez-Dolan) is indeed giving a finer form of locality, as explained by Dmitri Pavlov. However I think there are two quicke …
- 24.1k
79
votes
What is the motivation for a vertex algebra?
Vertex algebras precisely model the structure of "holomorphic one-dimensional algebra" -- in other words, the algebraic structure that you get if you try to formalize the idea of operators (elements o …
- 24.1k
3
votes
Accepted
Mirror symmetries for generalized geometries ?
Mirror symmetry is at the most fundamental level an isomorphism of N=(2,2)-supersymmetric conformal field theories attached to different geometric data, which acts on the supersymmetries as a prescrib …
- 24.1k
6
votes
About topological B model
This is the subject of this paper by Kevin Costello -- he constructs a solution to a master equation associated to a Calabi-Yau category, which one could take to be the category of branes in the topol …
- 24.1k
4
votes
Who can tell me the properties for the delta function in Sato's theory?
In addition to Kac's excellent book I thought I'd mention Vertex algebras and algebraic curves by Ed Frenkel and me, which goes a little more into formal delta functions, D-modules and the like --- se …
- 24.1k
14
votes
About state-field correspondence
I want to elaborate a little on Pavel's excellent answer.
We can think (very schematically) of local operators in an n-dimensional
field theory the following way. We have an n-1 manifold M with some …
- 24.1k
13
votes
Mirror symmetry mod p?! ... Physics mod p?!
The most interesting answer I know to this question is the recent work of Albert Schwarz with Vadim Vologodsky, Ilya Shaprio and Maxim Kontsevich, in which for example they use properties of the Frobe …
- 24.1k
15
votes
Accepted
Higher genus closed string B-model
This is a great question I wish I understood the answer to better.
I know two vague answers, one based on derived algebraic geometry and one based on string theory.
The first answer, that Costello exp …
- 24.1k