The nonperturbative functional renormalization group and its applications

N. Dupuis*, L. Canet, A. Eichhorn, W. Metzner, J. M. Pawlowski, M. Tissier, N. Wschebor

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Abstrakt

The renormalization group plays an essential role in many areas of physics, both conceptually and as a practical tool to determine the long-distance low-energy properties of many systems on the one hand and on the other hand search for viable ultraviolet completions in fundamental physics. It provides us with a natural framework to study theoretical models where degrees of freedom are correlated over long distances and that may exhibit very distinct behavior on different energy scales. The nonperturbative functional renormalization-group (FRG) approach is a modern implementation of Wilson's RG, which allows one to set up nonperturbative approximation schemes that go beyond the standard perturbative RG approaches. The FRG is based on an exact functional flow equation of a coarse-grained effective action (or Gibbs free energy in the language of statistical mechanics). We review the main approximation schemes that are commonly used to solve this flow equation and discuss applications in equilibrium and out-of-equilibrium statistical physics, quantum many-particle systems, high-energy physics and quantum gravity.

OriginalsprogEngelsk
TidsskriftPhysics Reports
Vol/bind910
Sider (fra-til)1-114
ISSN0370-1573
DOI
StatusUdgivet - 10. maj 2021

Bibliografisk note

Funding Information:
L. C. acknowledges support from Institut Universitaire de France and from ANR through the project NeqFluids (grant ANR-18-CE92-0019 ). A. E. is supported by the DFG under grant no. Ei-1037/1 , by a research grant ( 29405 ) from VILLUM FONDEN , and also partially supported by a visiting fellowship at the Perimeter Institute for Theoretical Physics. L. C., M. T. and N. W. acknowledge support from the program ECOS Sud U17E01 and from IRP “Institut Franco-Uruguayen de Physique”. N. W. is supported by Grant I+D number 412 of the CSIC (UdelaR) Commission and Programa de Desarrollo de las Ciencias Básicas (PEDECIBA). J.M.P. acknowledges support by the DFG under Germany’s Excellence Strategy EXC 2181/1 - 390900948 (the Heidelberg STRUCTURES Excellence Cluster), the DFG Collaborative Research Centre SFB 1225 ( ISOQUANT ), and the BMBF grant 05P18VHFCA .

Funding Information:
We have benefited from collaborations and discussions with many people. In particular we are grateful to Sabine Andergassen, Ivan Balog, Jean-Paul Blaizot, Federico Benitez, Jens Braun, Anton Cyrol, Bertrand Delamotte, Gonzalo De Polsi, Sebastian Diehl, Andreas Eberlein, Wei-jie Fu, Thomas Gasenzer, Holger Gies, Aaron Held, Carsten Honerkamp, Yuji Igarashi, Katsumi Itoh, Pawel Jakubczyk, Thomas Kloss, Tim Koslowski, Daniel Litim, Volker Meden, Mario Mitter, Dominique Mouhanna, Carlo Pagani, Marcela Pel?ez, Roberto Percacci, Antonio Pereira, Alessia Platania, Adam Ran?on, Manuel Reichert, Fabian Rennecke, Martin Reuter, F?lix Rose, Manfred Salmhofer, Frank Saueressig, Bernd-Jochen Schaefer, Michael Scherer, Kurt Sch?nhammer, Lorenz von Smekal, Davide Squizzato, Nils Strodthoff, Gilles Tarjus, Malo Tarpin, Arno Tripolt, Demetrio Vilardi, Christof Wetterich, Nicolas Wink, Masatoshi Yamada and Hiroyuki Yamase. We also thank Bertrand Delamotte and D. Benedetti, the organizers of the conference ERG2018, who suggested the writing of this review. L. C. acknowledges support from Institut Universitaire de France and from ANR through the project NeqFluids (grant ANR-18-CE92-0019). A. E. is supported by the DFG under grant no. Ei-1037/1, by a research grant (29405) from VILLUM FONDEN, and also partially supported by a visiting fellowship at the Perimeter Institute for Theoretical Physics. L. C. M. T. and N. W. acknowledge support from the program ECOS Sud U17E01 and from IRP ?Institut Franco-Uruguayen de Physique?. N. W. is supported by Grant I+D number 412 of the CSIC (UdelaR) Commission and Programa de Desarrollo de las Ciencias B?sicas (PEDECIBA). J.M.P. acknowledges support by the DFG under Germany's Excellence Strategy EXC 2181/1 - 390900948 (the Heidelberg STRUCTURES Excellence Cluster), the DFG Collaborative Research Centre SFB 1225 (ISOQUANT), and the BMBF grant 05P18VHFCA.

Publisher Copyright:
© 2021 Elsevier B.V.

Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.

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