Discrete<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>R</mml:mi></mml:math>-symmetry anomalies in heterotic orbifold models

Abstract

Anomalies of discrete $R$ symmetries appearing in heterotic orbifold models are studied. We find that the mixed anomalies for different gauge groups satisfy the universal Green-Schwarz condition, indicating that these anomalies are canceled by the Green-Schwarz mechanism. An exact relation between the anomaly coefficients of the discrete $R$ symmetries and one-loop beta-function coefficients is obtained. We also find that the discrete $R$ symmetries have a good chance to be unbroken down to the supersymmetry breaking scale. Even below this scale a ${Z}_{2}$ subgroup is unbroken, and it may be an origin of the $R$ parity of the minimal supersymmetric standard model. Relations between the $R$-symmetry anomalies and $T$-duality anomalies are also investigated.