Lorentz symmetry from a random Hamiltonian

We match the density of energy eigenstates of a local field theory with that of a random Hamiltonian order by order in a Taylor expansion. In our previous work we assumed Lorentz symmetry of the field theory, which entered through the dispersion relation. Here we extend that work to consider a generalized dispersion relation and show that the Lorentz symmetric case is preferred, in that the Lorentz symmetric dispersion relation gives a better approximation to a random Hamiltonian than the other local dispersion relations we considered.Comment: 8 pages, 6 figures. V2: Final version accepted for publication in PRD. Discussion improved throughout, including clarification of the fact that we address our key questions only at the level of the dispersion relation. No change to our technical work or result

Non-perturbative Unitarity of Gravitational Higgs Mechanism

In this paper we discuss massive gravity in Minkowski space via gravitational Higgs mechanism, which provides a non-perturbative definition thereof. Using this non-perturbative definition, we address the issue of unitarity by studying the full nonlinear Hamiltonian for the relevant metric degrees of freedom. While perturbatively unitarity is not evident, we argue that no negative norm state is present in the full nonlinear theory.Comment: 15 pages, Phys. Rev. D versio

Gravity on a 3-brane in 6D Bulk

We study gravity in codimension-2 brane world scenarios with infinite volume extra dimensions. In particular, we consider the case where the brane has non-zero tension. The extra space then is a two-dimensional ``wedge'' with a deficit angle. In such backgrounds we can effectively have the Einstein-Hilbert term on the brane at the classical level if we include higher curvature (Gauss-Bonnet) terms in the bulk. Alternatively, such a term would be generated at the quantum level if the brane matter is not conformal. We study (linearized) gravity in the presence of the Einstein-Hilbert term on the brane in such backgrounds. We find that, just as in the original codimension-2 Dvali-Gabadadze model with a tensionless brane, gravity is almost completely localized on the brane with ultra-light modes penetrating into the bulk.Comment: 16 pages, revtex; references added (to appear in Phys. Lett. B

Massive Gravity in de Sitter Space via Gravitational Higgs Mechanism

In this paper we discuss massive gravity in de Sitter space via gravitational Higgs mechanism, which provides a nonlinear definition thereof. The Higgs scalars are described by a nonlinear sigma model, which includes higher derivative terms required to obtain the Fierz-Pauli mass term. Using the aforesaid non-perturbative definition, we address appearance of an enhanced local symmetry and a null norm state in the linearized massive gravity in de Sitter space at the special value of the graviton mass to the Hubble parameter ratio. By studying full non-perturbative equations of motion, we argue that there is no enhanced symmetry in the full nonlinear theory. We then argue that in the full nonlinear theory no null norm state is expected to arise at the aforesaid special value. This suggests that no ghost might be present for lower graviton mass values and the full nonlinear theory might be unitary for all values of the graviton mass and the Hubble parameter with no van Dam-Veltman-Zakharov discontinuity. We argue that this is indeed the case by studying full nonlinear Hamiltonian for the relevant conformal and helicity-0 longitudinal modes. In particular, we argue that no negative norm state is present in the full nonlinear theory.Comment: 22 pages, comments and references added. Phys.Rev.D versio

Diluting solutions of the cosmological constant problem

We discuss the cosmological constant problem in the context of higher codimension brane world scenarios with infinite-volume extra dimensions.Comment: 11 pages, Revtex, reference adde

Toward Solving the Cosmological Constant Problem?

We discuss the cosmological constant problem in the context of higher codimension brane world scenarios with infinite-volume extra dimensions. In particular, by adding higher curvature terms in the bulk action we are able to find smooth solutions with the property that the 4-dimensional part of the brane world-volume is flat for a range of positive values of the brane tension.Comment: 45 pages, revtex, 8 eps figure