5-dimensional Chern-Simons gauge theory on an interval: Massive spin-2 theory from symmetry breaking via boundary conditions
Mahdi Torabian (Department of Physics, Sharif University of Technology, Azadi Ave, 1458889694, Tehran, Iran)
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 . 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 ) KK gravitons are determined as . The 4-dimensional Planck mass is and we find the hierarchy .