Graviton propagation in an asymmetric warped background: Lorentz violation and the null energy condition

Shahrokh Parvizi,Hossein Rezaee

doi:10.1007/jhep08(2014)076

Abstract

The graviton propagation in an asymmetric background is studied. The background is a configuration in the six-dimensional Salam-Sezgin model, in which a 3-form H-field turned on [JHEP 0910 (2009) 086]. The compact dimensions form a cylindrical space with branes as boundaries. The background gets asymmetry due to the H-field and violates the Lorentz symmetry. We derive the graviton equation in this background and show that it gets massless mode traveling with superluminal speed. A tower of K-K modes exists with a mass gap. On the other hand, it is known that breaking the Lorentz symmetry on an asymmetric background is constrained by the null energy condition. This no-go theorem doesn’t work well in six-dimensional space-times and by this model we provide a counterexample for which the null energy condition is satisfied while the Lorentz symmetry is gravitationally violated.

Highlights

This no-go theorem doesn’t work well in six-dimensional space-times and by this model we provide a counterexample for which the null energy condition is satisfied while the Lorentz symmetry is gravitationally violated
We have considered the dispersion relation for gravitational wave in the six-dimensional space compactified to 4D, in the presence of dilaton and an electric H field
The dispersion relation seems to depend on the charge and the dilaton coupling constant as well as an additional integration constant to be fine-tuned in the model

Summary

The set-up

We give a brief introduction to the model in [27]. Let us begin by the bosonic part of Salam-Sezgin Lagrangian as. Inserting the metric ansatz into field equations (2.2), a natural gauge condition for fixing parameter z seems to be w + 3a − v + b = 0 that leads to following solution:. (2.6) could not essentially reduce to these limiting solutions, unless the constants zi’s are chosen properly. This can be done by rewriting, for example, e−x in (2.6) as e−x = √ qeλ(|z|+z1) − e−λ(|z|+z1) =. Where Tp(TLp) stands for tension of p−brane located at z = 0(z = L) and tilde denotes density of tension In this configuration, 4-branes are boundaries of the space and 3 and zero branes are smeared over 4-branes.

The null energy condition

Small space-time fluctuations

Numerical results

Conclusion