A Comment on Brane Bending and Ghosts in Theories with Infinite Extra Dimensions

Theories with infinite extra dimensions open exciting opportunities for particle physics. We argued recently that along with attractive features there are phenomenological difficulties in this class of models. In fact, there is no graviton zeromode in this case and 4D gravity is obtained by means of continuum bulk modes. These modes have extra polarization degrees of freedom which do not decouple at low energies and lead to inconsistent predictions for light bending and Mercury perihelion. In recent papers, [hep-th/0003020] and [hep-th/0003045] the authors made use of brane bending in order to cancel the unwanted physical polarization of gravitons. In this note we point out that this mechanism does not solve the problem since it uses a ghost which cancels the extra degrees of freedom. In order to have a consistent model the ghost should be eliminated. As soon as this is done the 4D gravity becomes unconventional and contradicts to General Relativity. We also comment on a naive expectation that the theory at large distances becomes 5-dimensional and that ghosts could decay. New mechanisms are needed to remedy these models. It is very attractive to have theories with infinite extra dimensions. The following 5D warped metric serves as a good example of this class of models: ds = A(y)ημν dx dx − dy , (1) where the warp factor A(y) tends to a nonzero constants at ±∞. A brane setup which realizes this was recently proposed in Ref. [1]. It was argued in Refs. [2] and [3] that these models are very attractive since they could give new insights into bulk supersymmetry and the cosmological constant problem. Regretfully, as they stand right now, these theories encounter two serious challenges, to reproduce the correct four-dimensional Einstein limit without invoking ghost states [2] and to satisfy a weak energy positivity condition [3]. The aim of the present note is to respond to the criticism of [4] and [5] regarding the first issue. Let us first recall the arguments of Ref. [2]. The work was based on the following assumptions: I) The theory is selfconsistent in the sense that has no unconventional or unphysical states such as ghosts; II) 5D gravity couples universally to the energy-momentum tensor Tμν . We argue that in [4] and [5] the condition (I) is relaxed. In models with infinite extra dimensions, unlike the Randall-Sundrum (RS) model [6], there is no localized 4D spin-2 or spin-0 zero-mode. The only relevant physical degrees of freedom are 4D massive spin-2 gravitons. As a result, the 4D gravity is obtained by exchanging a metastable graviton [1, 7, 2]. This is equivalent to the exchange of a continuum of massive spin-2 bulk states. Each of the continuum states, from the 4D point of view, have strictly 5 physical degrees of freedom. These can be conveniently decomposed as: 2 from 4D massless graviton, 2 from “graviphoton” and 1 for a “graviscalar”. Two of these, coming from the “graviphotons”are nor relevant for the matter localized on the brane. Graviscalars contribute to physical processes [8, 9]. These extra scalar degrees of freedom lead to deviations from the standard predictions of Einstein’s theory [8, 9, 2] since the tensor structures of massive and massless gravitons are different: ( 1 2 (ηη + ηη)− 1 3 ηη +O(p) )