Duality Anomaly Cancellation, Minimal String Unification and the Effective Low-Energy Lagrangian of 4-D Strings

TL;DR

This paper systematically studies duality anomaly cancellations in 4-D orbifold string models, constraining massless spectra and implications for string unification and low-energy gauge couplings.

Contribution

It classifies modular weights in Abelian orbifolds and shows how anomaly cancellation constrains the massless fermion content, impacting model building.

Findings

Certain orbifolds cannot realize the MSSM spectrum without anomalies.

Duality anomalies relate to string threshold corrections for gauge couplings.

Minimal scenarios exclude specific Z_N orbifolds like Z_3 and Z_7.

Abstract

We present a systematic study of the constraints coming from target-space duality and the associated duality anomaly cancellations on orbifold-like 4-D strings. A prominent role is played by the modular weights of the massless fields. We present a general classification of all possible modular weights of massless fields in Abelian orbifolds. We show that the cancellation of modular anomalies strongly constrains the massless fermion content of the theory, in close analogy with the standard ABJ anomalies. We emphasize the validity of this approach not only for (2,2) orbifolds but for (0,2) models with and without Wilson lines. As an application one can show that one cannot build a ${\bf Z}_3$ or ${\bf Z}_7$ orbifold whose massless charged sector with respect to the (level one) gauge group $SU(3)\times SU(2) \times U(1)$ is that of the minimal supersymmetric standard model, since any such model would necessarily have duality anomalies. A general study of those constraints for Abelian orbifolds is presented. Duality anomalies are also related to the computation of string threshold corrections to gauge coupling constants. We present an analysis of the possible relevance of those threshold corrections to the computation of $\sin^2\theta_W$ and $\alpha_3$ for all Abelian orbifolds. Some particular {\it minimal} scenarios, namely those based on all ${\bf Z}_N$ orbifolds except ${\bf Z}_6$