One-loop diagrams in quantum gravity coupled to scalar electrodynamics

Abstract

In nonsupersymrnetric-covariant quantum gravity theory, for each system of gravity coupled with single field is one-loop divergent. There were two kinds of methods to reach this result: diagrammatic calculation and heat kernel expansion. On the other hand, more symmetry requirements make the theory finite and it was analyzed how it is possible. In this paper, based on diagrammatic calculation, we consider Einstein-Scalar electrodynamics (Einstein-SQED) system which is the simplest model among the systems of gravity coupled with multiple fields having their own interaction. Although it is known that fermionic loop can cancel the divergent terms as in the case of supersymmetric, theory, there might be accidental cancellation by the equation of motion at a low probability. It is worth to study because there is no such attempt for this model yet and it can be checked easily using the existing result. We introduce how to calculate the possible one-loop diagrams in Einstein-SQED system and show how divergent terms are not vanished with the results calculated earlier.