Localization of Quantum Fields on Branes

TL;DR

This paper investigates how quantum fields can be localized on branes within higher-dimensional spaces, analyzing stability and boundary conditions in Minkowski and AdS backgrounds, and showing the induced fields can mimic standard lower-dimensional physics.

Contribution

It introduces a mechanism for localizing quantum fields on branes with boundary conditions, analyzing stability and spectral properties in Minkowski and AdS spaces, and demonstrating the induced fields can replicate familiar physics.

Findings

Stable quantum fields on branes are achievable with specific boundary conditions.

In AdS space, the spectral function can feature massive excitations.

The induced brane fields can mimic standard lower-dimensional physics.

Abstract

A mechanism for localization of quantum fields on a $s$-brane, representing the boundary of a s+2 dimensional bulk space, is investigated. Minkowski and AdS bulk spaces are analyzed. Besides the background geometry, the relevant parameters controlling the theory are the mass M and a real parameter \eta, specifying the boundary condition on the brane. The importance of exploring the whole range of allowed values for these parameters is emphasized. Stability in Minkowski space requires \eta to be greater or equal to -M, whereas in the AdS background all real \eta are permitted. Both in the flat and in AdS case, the induced field on the brane is a non-canonical generalized free field. For a suitable choice of boundary condition, corresponding to the presence of a boundary state, the induced field on the brane mimics standard s+1 dimensional physics. In a certain range of \eta, the spectral function in the the AdS case is ominated by a massive excitation, which imitates the presence of massive particle on the brane. We show that the quantum field induced on the brane is stable.