Abstract
We compute one-loop quantum corrections to gravitational couplings in the effective action of four-dimensional heterotic strings where supersymmetry is spontaneously broken by Scherk–Schwarz fluxes. We show that in both heterotic and type II theories of this class, no moduli dependent corrections to the Planck mass are generated. We explicitly compute the one-loop corrections to the R2 coupling and find that, despite the absence of supersymmetry, its contributions may still be organised into representations of subgroups of the modular group, and admit a universal form, determined uniquely by the multiplicities of the ground states of the theory. Moreover, similarly to the case of gauge couplings, also the gravitational sector may become strongly coupled in models which dynamically induce large volume for the extra dimensions.
Highlights
Supersymmetry is undoubtedly one of the central ingredients of String Theory
Including such corrections essentially calls for supersymmetry to be spontaneously broken from the very beginning, in the framework of a fully-fledged string theory
The purpose of this paper is to examine the structure of one-loop threshold corrections to gravitational R2 couplings in heterotic theories with spontaneously broken supersymmetry1
Summary
Supersymmetry is undoubtedly one of the central ingredients of String Theory. Many of its spectacular results, such as duality connections, or various non-renormalisation theorems for string amplitudes, rely heavily on its presence. The purpose of this paper is to examine the structure of one-loop threshold corrections to gravitational R2 couplings in heterotic theories with spontaneously broken supersymmetry1 To this end, we employ the background field method of [62] which involves consistently deforming the flat non-supersymmetric theory by switching on an exact (1,1) integrable perturbation associated to a non-trivial but constant curvature R and obtaining the exact deformed partition function Z(R). We further find that one-loop corrections to the R2 term are non-trivial and may even lead the theory into a strong coupling regime in models that dynamically favour a large volume of their internal space In this way, the decompactification problem of gauge couplings and its gravitational counterpart furnish important constraints on model building.
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