5-Dimensional Chern-Simons Gauge Theory on an Interval: Massive Spin-2 Theory from Symmetry Breaking via Boundary Conditions

Abstract

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 $\zeta$ 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 $n<L{l}^{-1}$) KK gravitons $m_{\mathrm{KK}}^{(n)}$ are determined as $m=(\zeta L^{-1}{)}^{\frac{1}{2}}\ll m_{\mathrm{KK}}^{(n)}=n{L}^{-1}$. The 4-dimensional Planck mass is $m_{\mathrm{Pl}}\sim (L{l}^{-3}{)}^{\frac{1}{2}}$ and we find the hierarchy $\zeta <m<L^{-1}<l^{-1}<m_{\mathrm{Pl}}$.

8 pages, published version

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Cited by in corpus (1)

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