Weyl invariance of the bosonic string in torsional Newton-Cartan geometry
Summary
We consider the closed bosonic string in Newton-Cartan geometry with Kalb-Ramond and dilaton matter. This theory is quantized with the background field quantization method. The theory is then no longer invariant under a Weyl transformation: there is an anomaly. To mend this we impose conditions on the spacetime fields. The Weyl anomaly can be parametrized by beta-functions of which we will focus on the dilaton beta-function, as this was the only beta-function not computed in a previous treatment. We find the contribution to the dilaton beta-function by considering two-loop Feynman diagrams. These diagrams are given and a general strategy to calculate them is provided.