期刊
COMMUNICATIONS IN MATHEMATICAL PHYSICS
卷 325, 期 2, 页码 367-419出版社
SPRINGER
DOI: 10.1007/s00220-013-1863-2
关键词
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资金
- NSF [PHY-0969448, PHY-0503584, PHY-0757647]
- Roger Dashen membership in the Institute for Advanced Study
- DOE [DE-FG03-92-ER40701]
- DARPA [HR0011-09-1-0015]
- National Science Foundation [PHY05-51164]
- Simons Center for Geometry and Physics
- Max Planck Institut fur Mathematik
We propose a dictionary between geometry of triangulated 3-manifolds and physics of three-dimensional gauge theories. Under this duality, standard operations on triangulated 3-manifolds and various invariants thereof (classical as well as quantum) find a natural interpretation in field theory. For example, independence of the SL(2) Chern-Simons partition function on the choice of triangulation translates to a statement that partition functions of two mirror 3d gauge theories are equal. Three-dimensional field theories associated to 3-manifolds can be thought of as theories that describe boundary conditions and duality walls in four-dimensional SCFTs, thus making the whole construction functorial with respect to cobordisms and gluing.
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