Finite soft terms in string compactifications with broken supersymmetry

We consider the role of supersymmetry breaking soft terms that are present in generalized Narain compactifications of heterotic string theory, in which local supersymmetry is spontaneously broken, with gravitino masses being inversely proportional to the radii of compact dimensions. Such compactifications and their variants, are thought to be the natural application of the Scherk-Schwarz mechanism to string theory. In this paper we show that in the case where this mechanism leads to spontaneous breaking of N = 4, d = 4 local supersymmetry, the limit κ → 0 yields a 2-parameter class of distinct, dimension ≤ 3 explicit soft terms whose precise form are shown to preserve the ultraviolet properties of N = 4 Super Yang-Mills theory. This result is in broad agreement with that of the field theory Scherk-Schwarz mechanism, as applied to N = 1, d = 10 supergravity coupled to Super Yang-Mills, although the detailed structure of the soft terms are different in general.