Generalized Framework for Auxiliary Extra Dimensions

TL;DR

This paper generalizes ghost-free boundary conditions in auxiliary extra dimension models of gravity, extends the formalism to multiple dimensions, and explores the inclusion of Gauss-Bonnet terms, maintaining ghost-free properties.

Contribution

It introduces a generalized boundary condition framework that avoids ghosts order-by-order and to all orders, extending the model to multiple auxiliary dimensions and including Gauss-Bonnet terms.

Findings

Boundary conditions can be adjusted to avoid ghosts at all orders.

Multi-dimensional models with rotationally invariant boundaries are equivalent to single auxiliary dimension models.

Inclusion of Gauss-Bonnet term preserves ghost-free properties.

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.