Alternative flow equation for the functional renormalization group

Abstract

We derive an alternative to the Wetterich-Morris-Ellwanger equation by means of the two-particle irreducible (2PI) effective action, exploiting the method of external sources due to Garbrecht and Millington. The latter allows the two-point source of the 2PI effective action to be associated consistently with the regulator of the renormalization group flow. We show that this procedure leads to a flow equation that differs from that obtained in the standard approach based on the average one-particle irreducible effective action.

6 pages, revtex format; amended to incorporate corrections from an erratum (submitted to PRD) that relate to the incorrect functional identity original reported for the inverse two-point function; conclusions otherwise unchanged

References in corpus (8)

• Exact evolution equation for the effective potential
• Asymptotic safety in the f(R) approximation
• Ghost anomalous dimension in asymptotically safe quantum gravity
• Aspects of asymptotic safety for quantum gravity
• Renormalization group methods and the 2PI effective action
• Visualising quantum effective action calculations in zero dimensions
• A new functional RG flow: regulator-sourced 2PI versus average 1PI
• Benchmarking regulator-sourced 2PI and average 1PI flow equations in zero dimensions

Cited by in corpus (9)

• The nonperturbative functional renormalization group and its applications
• Functional renormalization group and 2PI effective action formalism
• Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. I. The $O(N)$ model
• Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. II. Entropy production and irreversibility of RG flows
• Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. III. Shock and rarefaction waves in RG flows reveal limitations of the $N\to \infty$ limit in $O(N)$-type models
• Gauge dependence of alternative flow equation for the functional renormalization group
• Vertex functions and their flow equations from the 2PI effective action
• Basic properties of an alternative flow equation in gravity theories
• Benchmarking regulator-sourced 2PI and average 1PI flow equations in zero dimensions