Thermal/quantum effects and induced superstring cosmologies

TL;DR

This paper studies how thermal and quantum effects in superstring theories with broken supersymmetry induce cosmological evolution, leading to solutions where temperature, supersymmetry breaking scale, and universe expansion are interconnected.

Contribution

It provides a detailed analysis of one-loop thermal and quantum corrections in superstring models, showing how they generate a cosmological evolution with fixed ratios between key scales.

Findings

The ratio M/T remains constant during evolution.

Solutions include a Friedmann-Hubble equation with radiation and curvature terms.

The effective potential lifts the classical flatness of the supersymmetry-breaking modulus.

Abstract

We consider classical superstring theories on flat four dimensional space-times, and where N=4 or N=2 supersymmetry is spontaneously broken. We obtain the thermal and quantum corrections at the string one-loop level and show that the back-reaction on the space-time metric induces a cosmological evolution. We concentrate on heterotic string models obtained by compactification on a T^6 torus and on T^6/Z_2 orbifolds. The temperature T and the supersymmetry breaking scale M are generated via the Scherk-Schwarz mechanism on the Euclidean time cycle and on an internal spatial cycle respectively. The effective field theory corresponds to a no-scale supergravity, where the corresponding no-scale modulus controls the Susy-breaking scale. The classical flatness of this modulus is lifted by an effective thermal potential, given by the free energy. The gravitational field equations admit solutions where M, T and the inverse scale factor 1/a of the universe remain proportional. In particular the ratio M/T is fixed during the time evolution. The induced cosmology is governed by a Friedmann-Hubble equation involving an effective radiation term ~1/a^4 and an effective curvature term ~1/a^2, whose coefficients are functions of the complex structure ratio M/T.