Renormalization of the 4PI effective action using the functional renormalization group

Abstract

Techniques based on n-particle irreducible effective actions can be used to study systems where perturbation theory does not apply. The main advantage, relative to other non-perturbative continuum methods, is that the hierarchy of integral equations that must be solved truncates at the level of the action, and no additional approximations are needed. The main problem with the method is renormalization, which until now could only be done at the lowest (n=2) level. In this paper we show how to obtain renormalized results from an n-particle irreducible effective action at any order. We consider a symmetric scalar theory with quartic coupling in four dimensions and show that the 4 loop 4-particle-irreducible calculation can be renormalized using a renormalization group method. The calculation involves one bare mass and one bare coupling constant which are introduced at the level of the Lagrangian, and cannot be done using any known method by introducing counterterms. * carrington@brandonu.ca †

The nonperturbative functional renormalization group and its applications

“…the DSE or nPI solution for the same approximation, they will only agree if the given approximation leads to the same resummation of -nonperturbative -diagrams. This rarely happens, the only known examples are perturbation theory and self-consistent nPI schemes, [67,304,598,605,[743][744][745][746][747][748][749]. Moreover, even in the known examples, perturbation theory and nPI schemes, a comparison is only possible if taking into account the generically different RG scheme in the functional RG, for related work see [67,80,[82][83][84][85][86][87][88][89].…”

Functional renormalization group and 2PI effective action formalism

“…To proceed, we start with a detailed analysis of the diagrammatic content of Eq. (47), which is best unveiled by examining first the approximations to ∂ κ I κ up to L = 4 loops for Φ (i.e. two-loop for I).…”

“…What we use in this paper is rather a hybrid scheme, where we close the 1PI hierarchy of flow equations by using the 2PI relation between the two-point and four-point functions [39]. While the latter relation can be seen as part of the 2PI hierarchy, we do not focus on the 2PI n-point functions, as done for instance in [44] (see also [45,46,47], and similarly [48]), but rather on different objects, identified as loop truncations of the four-point function. These objects emerge naturally in the flow formulation of Φ-derivable approximations and turn out to play an important role in their renormalization, whether this is achieved through the flow equations or via the more standard diagrammatic approach.…”

Emergent Hadrons and Diquarks

“…Related fRG for n-particle irreducible (nPI) actions can be found in e.g. [24,[115][116][117][118][119][120][121][122][123][124][125].…”