Renormalization of the gravitational trace anomaly in QED

Abstract

We evaluate to $O({e}^{2})$ in QED the effect of the electromagnetic coupling on the gravitational trace anomaly. The basis of the discussion is the calculation of the absorptive part of $i〈0|T({\ensuremath{\theta}}_{\ensuremath{\mu}\ensuremath{\nu}}(x){\ensuremath{\theta}}_{\ensuremath{\sigma}\ensuremath{\tau}}(y))|0〉$. Using dimensional regularization we find as in the analogous calculation of $\ensuremath{\sigma}({e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\mathrm{hadrons})$ that the result is free of infrared singularities. By combining our results with those of Shore we are able to exhibit the complete gravitational trace anomaly to $O({e}^{2})$. The relationship of our results with the renormalization group is briefly discussed.