Efficient Evaluation of Effective Action in Radial Backgrounds

TL;DR

The paper presents a new method to accelerate the convergence of partial-wave sums in effective action calculations for radial backgrounds, demonstrated through QCD instanton determinant computations.

Contribution

A systematic approach using radial WKB series to improve convergence speed in effective action evaluations in radial fields.

Findings

Enhanced convergence rate in partial-wave sums

Successful application to QCD instanton determinants

Improved computational efficiency in radial background calculations

Abstract

Recently a new caculational scheme for effective actions in radial background fields was developed. The effective action is expressed as an infinite sum of partial-wave contributions, using the rotational symmetry of the system. The sum becomes convergent after proper regularization and renormalization, but the rate of convergence is rather slow. We introduce a systematic way of accelerating the rate of convergence. This method is based on a radial WKB series in the angular momentum cut-off. We demonstrate the power of this scheme by applying it to the calculation of instanton determinant in QCD.