Generalized Framework for Auxiliary Extra Dimensions

TL;DR

Berezhiani and Mirbabayi study gravity with an auxiliary extra dimension (AED) and show that by generalizing the boundary condition at the second boundary $u=1$ to a function $\hat{g}_{\mu\nu}(g_{\alpha\beta})$, ghost-free completions of the Fierz-Pauli mass term can be achieved in the decoupling limit. They perform a perturbative dimensional reduction to derive the 4D graviton potential and show that the original fixed boundary $\hat{g}_{\mu\nu}=\eta_{\mu\nu}$ yields a ghost at quartic order, while suitable boundary adjustments can remove the quartic (and potentially higher orders). They also extend the framework to multiple auxiliary dimensions and prove that, under rotationally invariant boundaries, the multi-D model is equivalent to the single-AED model, though this equivalence can fail when modifying the bulk action (e.g., Gauss-Bonnet terms or higher powers of $k_{\mu\nu}$). The paper analyzes Gauss-Bonnet extensions and shows that they do not generically cure the quartic ghost, but a careful boundary tuning remains a viable path to ghost-free behavior in the decoupling limit.

Abstract

The theory of gravity with an auxiliary extra dimension is known to give the ghost-free cubic completion of the Fierz-Pauli mass term in the decoupling limit. Our work generalizes the boundary condition in the auxiliary dimension that avoids ghosts order-by-order, and to all orders, in the decoupling limit. Furthermore, we extend the formalism to the case of many auxiliary dimensions, and we show that the multi-dimensional extension with the rotationally invariant boundaries of the bulk, is equivalent to the model with a single auxiliary dimension. The above constructions require the appropriate adjustment of the boundary condition, which we discuss in detail. The other possible extension of the original model by the Gauss-Bonnet term is studied as well.