Year: 2007
Type: article
Abstract: There 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 and 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.
Source: Classical and Quantum Gravity
Author: Jemal Guven
Institution: Universidad Nacional Autónoma de México
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2103052416