Gauged diffeomorphisms and hidden symmetries in Kaluza-Klein theories

Nov, 2006
24 pages
Published in:
  • Class.Quant.Grav. 24 (2007) 2825-2844
e-Print:
Report number:
  • SPIN-06-40,
  • ITP-UU-06-50

Citations per year

20072010201320162019310
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