Discretizing gravity in warped spacetime

Abstract

We investigate the discretized version of the compact Randall-Sundrum model. By studying the mass eigenstates of the lattice theory, we demonstrate that for warped space, unlike for flat space, the strong coupling scale does not depend on the IR scale and lattice size. However, strong coupling does prevent us from taking the continuum limit of the lattice theory. Nonetheless, the lattice theory works in the manifestly holographic regime and successfully reproduces the most significant features of the warped theory. It is even in some respects better than the KK theory, which must be carefully regulated to obtain the correct physical results. Because it is easier to construct lattice theories than to find exact solutions to GR, we expect lattice gravity to be a useful tool for exploring field theory in curved space.

Disassembling the clockwork mechanism

“…whereg µν = η µν + h µν . The 5D Einstein-Hilbert action is then given by For instance, in a linear dilaton background of the form X(y) = Y (y) = e −4ky , M j = (M 3 5 a) 1/2 e −3kja , whereas in a Randall-Sundrum geometry, X(y) = e −2ky , Y (y)=1, one finds M j = (M 3 5 a) 1/2 e −kja , in agreement with [37]. In both cases, the effective Planck scale on a given site depends exponentially on the position of the site.…”

A clockwork theory

“…Finally, let us consider the clockwork gravitons. (For deconstructions of gravity in general scenarios see [36,49] and for RS see [50].) Discretisation of the fifth dimension in the action in eq.…”

Deconstructing dimensions and massive gravity

“…Some of these issues can be addressed by allowing the extra dimension(s) to be warped. For interesting work along these lines see [9][10][11][12], however in this work we shall consider a flat extra dimension. Deconstruction can also be studied in a holographic context where each site is taken to have AdS asymptotics, in this case it may be possible to find other interaction terms that avoid the traditional problems of massive gravity [11].…”