Adiabatic Regularization for Gauge Field and the Conformal Anomaly

Understand

We construct the adiabatic regularization method for a $U(1)$ gauge field in a conformally flat spacetime by quantizing in the canonical formalism the gauge fixed $U(1)$ theory with mass terms for the gauge fields and the ghost fields.

• We show that the adiabatic expansion for the mode functions and the adiabatic vacuum can be defined in a similar way using WKB-type solutions as the scalar fields.
• As an application of the adiabatic method, we compute the trace of the energy momentum tensor and reproduces the known result for the conformal anomaly obtained by the other regularization methods.
• The availability of the adiabatic expansion scheme for gauge field allows one to study the renormalization of the de-Sitter space maximal superconformal Yang-Mills theory using the adiabatic regularization method.