5-dimensional Chern-Simons gauge theory on an interval: Massive spin-2 theory from symmetry breaking via boundary conditions

In this note, we revisit the 4-dimensional theory of massive gravity through compactification of an extra dimension and geometric symmetry breaking. We dimensionally reduce the 5-dimensional topological Chern-Simons gauge theory of (anti) de Sitter group on an interval. We apply non-trivial boundary conditions at the endpoints to break all of the gauge symmetries. We identify different components of the gauge connection as invertible vierbein and spin-connection to interpret it as a gravitational theory. The effective field theory in four dimensions includes the dRGT potential terms and has a tower of Kaluza-Klein states without massless graviton in the spectrum. The UV cut of the theory is the Planck scale of the 5-dimensional gravity l−1. If ζ is the scale of symmetry breaking and L is the length of the interval, then the masses of the lightest graviton m and the level n (for n<Ll−1) KK gravitons mKK(n) are determined as m=(ζL−1)12≪mKK(n)=nL−1. The 4-dimensional Planck mass is mPl∼(Ll−3)12 and we find the hierarchy ζ<m<L−1<l−1<mPl.

Abstract licence: CC BY

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