Convenient Versus Unique Effective Action Formalism in 2D Dilaton-Maxwell Quantum Gravity

TL;DR

This paper compares convenient and unique effective action formalisms in 2D dilaton-Maxwell quantum gravity, analyzing one-loop divergences across gauges and discussing off-shell renormalizability, with extensions to dilaton-Yang-Mills gravity.

Contribution

It provides a detailed comparison of convenient and unique effective actions in 2D dilaton-Maxwell quantum gravity, including divergence calculations and renormalizability analysis.

Findings

On-shell effective action is finite and gauge-dependent.

Off-shell renormalizability depends on potential choices.

Extension to dilaton-Yang-Mills gravity demonstrated.

Abstract

The structure of one-loop divergences of two-dimensional dilaton-Maxwell quantum gravity is investigated in two formalisms: one using a convenient effective action and the other a unique effective action. The one-loop divergences (including surface divergences) of the convenient effective action are calculated in three different covariant gauges: (i) De Witt, (ii) $\Omega$-degenerate De Witt, and (iii) simplest covariant. The on-shell effective action is given by surface divergences only (finiteness of the $S$-matrix), which yet depend upon the gauge condition choice. Off-shell renormalizability is discussed and classes of renormalizable dilaton and Maxwell potentials are found which coincide in the cases of convenient and unique effective actions. A detailed comparison of both situations, i.e. convenient vs. unique effective action, is given. As an extension of the procedure, the one-loop effective action in two-dimensional dilaton-Yang-Mills gravity is calculated.