Quantum Dynamics of a Bulk-Boundary System

TL;DR

This paper investigates the quantum dynamics of a bulk-boundary system using the background field method, focusing on the Mirabelli-Peskin model, and introduces new regularization techniques, vacuum treatments, and analyzes the effective potential and Casimir energy.

Contribution

It presents a novel analysis of bulk-boundary quantum dynamics, including a new regularization method, a localized scalar field solution, and a supersymmetric effective potential at 1-loop level.

Findings

New regularization of momentum integrals proposed.

Localized scalar field solution found.

Supersymmetric effective potential computed at 1-loop.

Abstract

The quantum dynamics of a bulk-boundary theory is closely examined by the use of the background field method. As an example we take the Mirabelli-Peskin model, which is composed of 5D super Yang-Mills (bulk) and 4D Wess-Zumino (boundary). Singular interaction terms play an important role of canceling the divergences coming from the KK-mode sum. Some new regularization of the momentum integral is proposed. An interesting background configuration of scalar fields is found. It is a localized solution of the field equation. In this process of the vacuum search, we present a new treatment of the vacuum with respect to the extra coordinate. The "supersymmetric" effective potential is obtained at the 1-loop full (w.r.t. the coupling) level. This is the bulk-boundary generalization of the Coleman-Weinberg's case. Renormalization group analysis is done where the correct 4d result is reproduced. The Casimir energy is calculated and is compared with the case of the Kaluza-Klein model.