Supersymmetry from Boundary Conditions

TL;DR

This paper investigates supersymmetry breaking and restoration in five-dimensional theories through boundary conditions, comparing interval and orbifold approaches, and explores their implications for super Yang-Mills and warped backgrounds.

Contribution

It provides a detailed comparison of boundary condition methods in 5D supersymmetric theories, including wavefunction jumps, Scherk-Schwarz effects, and applications to super Yang-Mills and warped geometries.

Findings

Derived boundary conditions from action principles and orbifold parities.

Computed wavefunction jump profiles for general brane mass terms.

Showed supersymmetry can be preserved with tuning of boundary actions.

Abstract

We study breaking and restoration of supersymmetry in five-dimensional theories by determining the mass spectrum of fermions from their equations of motion. Boundary conditions can be obtained from either the action principle by extremizing an appropriate boundary action (interval approach) or by assigning parities to the fields (orbifold approach). In the former, fields extend continuously from the bulk to the boundaries, while in the latter the presence of brane mass-terms cause fields to jump when one moves across the branes. We compare the two approaches and in particular we carefully compute the non-trivial jump profiles of the wavefunctions in the orbifold picture for very general brane mass terms. We also include the effect of the Scherk-Schwarz mechanism in either approach and point out that for a suitable tuning of the boundary actions supersymmetry is present for arbitrary values of the Scherk-Schwarz parameter. As an application of the interval formalism we construct bulk and boundary actions for super Yang-Mills theory. Finally we extend our results to the warped Randall-Sundrum background.