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.

Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases - Part I: The $O(N)$ model

“…Zerodimensional field theory was also used to study densityfunctional theory [55,56,58] and applied to fermionic fields [53]. Recently, it was used to study and visualize 2PI effective actions [59] -also in the FRG framework [60,62,63].…”

Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases - Part III: Shock and rarefaction waves in RG flows reveal limitations of the $N \rightarrow \infty$ limit in $O(N)$-type models

“…For related works on this toy model QFT, we again refer to Refs. [3,24,[33][34][35][36][37][38][39][40][41][42][43][44][45][48][49][50][51][52][53][54].…”

“…Refs. [3,24,33,[35][36][37][38][39][40][41][42][43][44][45][46][47]. Even a lot of aspects of the large-/infinite-N limit have been discussed already within this setup, cf.…”

Gauge dependence of alternative flow equation for the functional renormalization group

“…Some years ago it was proposed [11] to realize main ideas of the FRG approach using concept of effective action with composite operators or, in another words, effective two-particle irreducible effective action introduced in paper [12] and then studied for gauge theories from point of view the gauge dependence in [13]. Quite recently the alternative flow equation using slightly different way in comparison with [11] has been introduced [14]. In standard perturbation approach to quantum theory of gauge fields the effective actions with composite operators used in [11,14] are gauge independent on-shell.…”

“…Quite recently the alternative flow equation using slightly different way in comparison with [11] has been introduced [14]. In standard perturbation approach to quantum theory of gauge fields the effective actions with composite operators used in [11,14] are gauge independent on-shell. But by itself this property does not guarantee the gauge independence of the effective action with composite operators found as non-perturbative solution to the flow equation as it was shown in the case of standard FRG approach [1].…”