Partial summation of the nonlocal expansion for the gravitational effective action in 4 dimensions

TL;DR

This paper introduces a method to partially sum the nonlocal expansion of the gravitational effective action in four dimensions by focusing on Weyl-tensor invariants, simplifying calculations related to vacuum gravitational effects.

Contribution

It demonstrates that a change of basis to Weyl-tensor invariants allows partial summation of the nonlocal expansion, reducing the required form factors to those of the Weyl tensor.

Findings

Explicit expression for the partially summed action

Simplifications in vertex function calculations

Application to vacuum gravitational wave effects

Abstract

The vacuum action for the gravitational field admits a known expansion in powers of the Ricci tensor with nonlocal operator coefficients (form factors). We show that going over to a different basis of curvature invariants makes possible a partial summation of this expansion. Only the form factors of the Weyl-tensor invariants need be calculated. The full action is then uniquely recovered to all orders from the knowledge of the trace anomaly. We present an explicit expression for the partially summed action, and point out simplifications resulting in the vertex functions. An application to the effect of the vacuum gravitational waves is discussed.