Gauge theories labelled by three-manifolds
type: Item
instance of: scholarly article
title: Gauge theories labelled by three-manifolds
zbMATH Open document ID: 1292.57012
author: Davide Gaiotto
author: Sergei Gukov
author: Tudor Dan Dimofte
published in: Communications in Mathematical Physics
publication date: 2014-01-24T00:00:00Z
full work available at URL: https://arxiv.org/abs/1108.4389
full work available at URL: CaltechAUTHORS:20140210-154717900
review text: This paper describes a conjectural relation between three dimensional manifolds with a certain type of boundary data and three dimensional field theories. To a surface, one may associate the moduli of flat \(\text{SL}_2\mathbb{C}\) connections modulo gauge transformation. This space has a natural symplectic structure. The boundary data associated to a \(3\)-manifold is exactly a polarization of the moduli space of the boundary. This may be understood via an ideal triangulation of the \(3\)-manifold with boundary coming from unpaired faces of the tetrahedra, and from the links of the ideal tetrahedra. The theory is then specified by describing the edge parameters, and associated polarizations for one tetrahedron together with the gluing laws. It is not surprising that \(\text{SL}_2\mathbb{Z}\) acts on the space of polarizations. An analogous action on the space of Lagrangian densities leads to the set of field theories associated to \(3\)-manifolds. For example the \(T\) matrix replaces a Lagrangian \(\mathcal{L}\) with \(\mathcal{L}+\frac{1}{4\pi}A\wedge dA\). A specific field theory is associated to a single tetrahedron, and then a gluing procedure is given to describe new theories by gluing existing theories.
reviewed by: David Auckly
Mathematics Subject Classification ID: 57M99
Mathematics Subject Classification ID: 81Q60
Mathematics Subject Classification ID: 81T13
zbMATH DE Number: 6249788
zbMATH Keywords: Field Theory
zbMATH Keywords: three manifold
zbMATH Keywords: invariant
MaRDI profile type: Publication
OpenAlex ID: W1990274428
arXiv ID: 1108.4389
Wikidata QID: Q56057583
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DOI: 10.1007/S00220-013-1863-2
description: scientific article; zbMATH DE number 6249788