Equivalent effective Lagrangians for Scherk-Schwarz compactifications

We discuss the general form of the mass terms that can appear in the effective field theories of coordinate-dependent compactifications à la Scherk-Schwarz. As an illustrative example, we consider an interacting five-dimensional theory compactified on the orbifold S1/Z2, with a fermion subject to twisted periodicity conditions. We show how the same physics can be described by equivalent effective Lagrangians for periodic fields, related by field redefinitions and differing only in the form of the five-dimensional mass terms. In a suitable limit, these mass terms can be localized at the orbifold fixed points. We also show how to reconstruct the twist parameter from any given mass terms of the allowed form. Finally, after mentioning some possible generalizations of our results, we re- discuss the example of brane-induced supersymmetry breaking in five-dimensional Poincar ́e supergravity, and comment on its relation with gaugino condensation in M-theory.