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

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

1992-02-14

arxiv.org/abs/hep-th/9202046v1

Nucl.Phys.B382:305-364,1992

Physics

High Energy Physics

High Energy Physics - Theory

69 pages

Scientific paper

10.1016/0550-3213(92)90189-I

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 ${\bf Z}_6$

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