Abelian Duality at Higher Genus
arXiv:1405.2483 · doi:10.1007/JHEP07(2014)157
Abstract
In three dimensions, a free, periodic scalar field is related by duality to an abelian gauge field. Here I explore aspects of this duality when both theories are quantized on a Riemann surface of genus g. At higher genus, duality involves an identification of winding with momentum on the Jacobian variety of the Riemann surface. I also consider duality for monopole and loop operators on the surface and exhibit the operator algebra, a refinement of the Wilson-'t Hooft algebra.
arXiv comment53 pages, 1 figure, v2: references added
References in corpus (8)
- Target Space Duality in String Theory
- Duality, Quotients, and Currents
- Topological Disorder Operators in Three-Dimensional Conformal Field Theory
- Monopole Operators and Mirror Symmetry in Three Dimensions
- Aspects of 3d N=2 Chern-Simons-Matter Theories
- The Uncertainty of Fluxes
- Heisenberg Groups and Noncommutative Fluxes
- Exact results for supersymmetric abelian vortex loops in 2+1 dimensions