String Threshold corrections in models with spontaneously broken supersymmetry

TL;DR

This paper investigates threshold corrections in heterotic models with spontaneously broken N=4 supersymmetry to N=2, revealing multiple universality classes and detailed moduli-dependent behaviors due to the structure of the elliptic genus.

Contribution

It provides a detailed analysis of one-loop threshold corrections in N=2 heterotic models with spontaneous N=4 to N=2 breaking, highlighting new universality classes and singularity structures.

Findings

Threshold corrections fall into several universality classes.

Threshold corrections exhibit singularities along rational lines of T^2 moduli.

Corrections have logarithmic singularities at large radii.

Abstract

We analyse a class of four-dimensional heterotic ground states with N=2 space-time supersymmetry. From the ten-dimensional perspective, such models can be viewed as compactifications on a six-dimensional manifold with SU(2) holonomy, which is locally but not globally K3 x T^2. The maximal N=4 supersymmetry is spontaneously broken to N=2. The masses of the two massive gravitinos depend on the (T,U) moduli of T^2. We evaluate the one-loop threshold corrections of gauge and R^2 couplings and we show that they fall in several universality classes, in contrast to what happens in usual K3 x T^2 compactifications, where the N=4 supersymmetry is explicitly broken to N=2, and where a single universality class appears. These universality properties follow from the structure of the elliptic genus. The behaviour of the threshold corrections as functions of the moduli is analysed in detail: it is singular across several rational lines of the T^2 moduli because of the appearance of extra massless states, and suffers only from logarithmic singularities at large radii. These features differ substantially from the ordinary K3 x T^2 compactifications, thereby reflecting the existence of spontaneously-broken N=4 supersymmetry. Although our results are valid in the general framework defined above, we also point out several properties, specific to orbifold constructions, which might be of phenomenological relevance.