Anomalies and discrete torsion in Type II and Type I worldsheet theories

Abstract

We provide a comprehensive study of anomalies and discrete torsion in the worldsheet theories of Type II and Type I string theories on a general ten-dimensional target space. In the modern understanding, the anomaly of a worldsheet theory is characterized by an invertible field theory in three dimensions, and invertible field theories are classified by the Anderson dual of a suitable bordism theory. To study the anomaly cancellation condition, we employ the explicit model of the Anderson dual constructed by Yamashita and Yonekura. We find that, for both Type II and Type I string theories, the anomaly of the worldsheet theory is cancelled if and only if the target space is orientable and admits a spin structure. We also determine the discrete torsion and clarify its physical meaning. It includes the distinctions between Type IIA and Type IIB string theories and between ordinary Type I and Sugimoto string theories.