Chern-Simons theory and three-dimensional surfaces

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dc.creatorGuven, Jemal
dc.date2006-11-14
dc.date2007-03-06
dc.date.accessioned2026-07-07T11:23:06Z
dc.date.available2026-07-07T11:23:06Z
dc.descriptionThere are two natural Chern-Simons theories associated with the embedding of a three-dimensional surface in Euclidean space; one is constructed using the induced metric connection -- it involves only the intrinsic geometry, the other is extrinsic and uses the connection associated with the gauging of normal rotations. As such, the two theories appear to describe very different aspects of the surface geometry. Remarkably, at a classical level, they are equivalent. In particular, it will be shown that their stress tensors differ only by a null contribution. Their Euler-Lagrange equations provide identical constraints on the normal curvature. A new identity for the Cotton tensor is associated with the triviality of the Chern-Simons theory for embedded hypersurfaces implied by this equivalence. The corresponding null surface stress capturing this information will be constructed explicitly.
dc.description10 pages, unnecessary details removed, typos fixed, references added
dc.identifierhttps://arxiv.org/abs/hep-th/0611144
dc.identifierhttp://arxiv.org/abs/hep-th/0611144
dc.identifierClass.Quant.Grav.24:1833-1840,2007
dc.identifierdoi:10.1088/0264-9381/24/7/009
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/194787
dc.subjectHigh Energy Physics - Theory
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectMathematical Physics
dc.titleChern-Simons theory and three-dimensional surfaces
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