One and two loop phenomenology in heterotic string theory

Abstract

We examine the phenomenological properties of certain heterotic string theories through the computation of one and two-loop amplitudes.

Initially, we consider the fate of shift-symmetries in effective string models is considered beyond tree-level. Such symmetries have been proposed in the past as a way to maintain a hierarchically small Higgs mass and also play a role in schemes of cosmological relaxation. It is argued that on general grounds one expects shift-symmetries to be restored in the limit of certain asymmetric compactifications, to all orders in perturbation theory. This behaviour is verified by explicit computation of the Kähler potential to one-loop order.

We then turn to the two-loop cosmological constant in non-supersymmetric heterotic strings where two independent criteria are presented that together guarantee its exponential suppression. They are derived by performing calculations in both the full string theory and in its effective field theory, and come respectively from contributions that involve only physical untwisted states, and contributions that include orbifold twisted states. The criteria depend purely on the spectrum and charges, so a model that satisfies them will do so with no fine-tuning. An additional consistency condition (emerging from the so-called separating degeneration limit of the two-loop diagram) is that the one-loop cosmological constant must also be suppressed, by Bose-Fermi degeneracy in the massless spectrum. We comment on the effects of the residual exponentially suppressed one-loop dilaton tadpole, with the conclusion that the remaining instability would be under perturbative control in a generic phenomenological construction. We remark that theories of this kind, that have continued exponential suppression to higher orders, can form the basis for a string implementation of the "naturalness without supersymmetry" idea.