Anomalies in Heterotic String and Decoupling Limit

We review the recent developments on the decoupling limit zooming in on a BPS string state in heterotic string theory. In this limit, the target-space geometry lacks any ten-dimensional metric description and acquires various non-Lorentzian features. We present the supersymmetric worldsheet sigma model in the decoupling limit. This sigma model describes the heterotic version of non-relativistic string theory, whose second quantization is related to heterotic matrix string theory. We introduce bookkeeping to separate the Yang–Mills gauge and gravitational anomaly analyses. We review the Yang–Mills gauge anomaly analysis in the sigma models before and after the decoupling limit is performed and provide further details on how the quantum calculation commutes with the decoupling limit. We comment on how the analogous calculation can be performed for the gravitational anomaly. This contribution is based on a talk at the University of Science and Technology of China.