Gauged diffeomorphisms and hidden symmetries in Kaluza-Klein theories
Nov, 200624 pages
Published in:
- Class.Quant.Grav. 24 (2007) 2825-2844
e-Print:
- hep-th/0611347 [hep-th]
Report number:
- SPIN-06-40,
- ITP-UU-06-50
View in:
Citations per year
Abstract:
We analyze the symmetries that are realized on the massive Kaluza-Klein modes in generic D-dimensional backgrounds with three non-compact directions. For this we construct the unbroken phase given by the decompactification limit, in which the higher Kaluza-Klein modes are massless. The latter admits an infinite-dimensional extension of the three-dimensional diffeomorphism group as local symmetry and, moreover, a current algebra associated to SL(D-2,R) together with the diffeomorphism algebra of the internal manifold as global symmetries. It is shown that the `broken phase' can be reconstructed by gauging a certain subgroup of the global symmetries. This deforms the three-dimensional diffeomorphisms to a gauged version, and it is shown that they can be governed by a Chern-Simons theory, which unifies the spin-2 modes with the Kaluza-Klein vectors. This provides a reformulation of D-dimensional Einstein gravity, in which the physical degrees of freedom are described by the scalars of a gauged non-linear sigma model based on SL(D-2,R)/SO(D-2), while the metric appears in a purely topological Chern-Simons form.- 11.30.Ly
- 04.50.+h
- 04.60.Kz
- Kaluza-Klein model
- higher-dimensional
- diffeomorphism: transformation
- transformation: gauge
- hidden symmetry
- dimensional reduction
- Chern-Simons term
References(40)
Figures(0)