Gauge Theories Labelled by Three-Manifolds
We propose a dictionary between geometry of triangulated 3-manifolds and physics of three-dimensional N = 2 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....
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Veröffentlicht in: | Communications in mathematical physics 2014, Vol.325 (2), p.367-419 |
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Hauptverfasser: | , , |
Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | We propose a dictionary between geometry of triangulated 3-manifolds and physics of three-dimensional
N
=
2
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
S
b
3
partition functions of two mirror 3d
N
=
2
gauge theories are equal. Three-dimensional
N
=
2
field theories associated to 3-manifolds can be thought of as theories that describe boundary conditions and duality walls in four-dimensional
N
=
2
SCFTs, thus making the whole construction functorial with respect to cobordisms and gluing. |
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ISSN: | 0010-3616 1432-0916 |
DOI: | 10.1007/s00220-013-1863-2 |