Functional renormalization group and 2PI effective action formalism

Abstract

We combine two non-perturbative approaches, one based on the two-particle-irreducible (2PI) action, the other on the functional renormalization group (fRG), in an effort to develop new non-perturbative approximations for the field theoretical description of strongly coupled systems. In particular, we exploit the exact 2PI relations between the two-point and four-point functions in order to truncate the infinite hierarchy of equations of the functional renormalization group. The truncation is "exact" in two ways. First, the solution of the resulting flow equation is independent of the choice of the regulator. Second, this solution coincides with that of the 2PI equations for the two-point and the four-point functions, for any selection of two-skeleton diagrams characterizing a so-called $\Phi$-derivable approximation. The transformation of the equations of the 2PI formalism into flow equations offers new ways to solve these equations in practice, and provides new insight on certain aspects of their renormalization. It also opens the possibility to develop approximation schemes going beyond the strict $\Phi$-derivable ones, as well as new truncation schemes for the fRG hierarchy.

80 pages, 22 figures

References in corpus (8)

• Exact evolution equation for the effective potential
• Non-existence of the Luttinger-Ward functional and misleading convergence of skeleton diagrammatic series for Hubbard-like models
• Renormalization group methods and the 2PI effective action
• Exact renormalization group and Phi-derivable approximations
• Renormalization group approach to interacting fermion systems in the two-particle-irreducible formalism
• Two-particle irreducible functional renormalization group schemes---a comparative study
• Renormalization of the 4PI effective action using the functional renormalization group
• On overlapping Feynman (sub)graphs

Cited by in corpus (17)

• Gauge Sector Dynamics in QCD
• Emergence of mass in the gauge sector of QCD
• Exploring smoking-gun signals of the Schwinger mechanism in QCD
• Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. I. The $O(N)$ model
• Bayesian inference of real-time dynamics from lattice QCD
• Gluon mass scale through the Schwinger mechanism
• Functional renormalization group for multilinear disordered Langevin dynamics II: Revisiting the $p=2$ spin dynamics for Wigner and Wishart ensembles
• Lectures in Quantum Gravity
• Coupling renormalization flow in the strongly interacting regime of an asymptotically free quantum field theory in four dimensions
• Large time effective kinetics $\beta$-functions for quantum (2+p)-spin glass
• Patterns of gauge symmetry in the background field method
• Topological Susceptibility in the Superconductive Phases of Quantum Chromodynamics: a Dyson-Schwinger Perspective
• Time-translation invariance symmetry breaking hidden by finite-scale singularities
• Functional renormalization with interaction flows: A single-boson exchange perspective and application to electron-phonon systems
• The quantum $p$-spin renormalization group in the large $N$ limit as a benchmark for functional renormalization group
• Spin liquid phase in the Hubbard model: Luttinger-Ward analysis of the slave-rotor formalism
• Benchmarking regulator-sourced 2PI and average 1PI flow equations in zero dimensions