Gradient Flow Exact Renormalization Group for Scalar Field Theories

[1] Y. Abe, Y. Hamada, and J. Haruna, Fixed point structure of the gradient flow exact

renormalization group for scalar field theories, PTEP 2022 no. 3, (2022) 033B03

[arXiv:2201.04111 [hep-th]].

[2] K. G. Wilson and J. B. Kogut, The Renormalization group and the epsilon

expansion, Phys. Rept. 12 (1974) 75–199.

[3] F. J. Wegner and A. Houghton, Renormalization group equation for critical

phenomena, Phys. Rev. A 8 (1973) 401–412.

[4] K. G. Wilson, The renormalization group and critical phenomena, Rev. Mod. Phys.

55 (1983) 583–600.

[5] J. Polchinski, Renormalization and Effective Lagrangians, Nucl. Phys. B 231 (1984)

269–295.

[6] C. Wetterich, Exact evolution equation for the effective potential, Phys. Lett. B 301

(1993) 90–94 [arXiv:1710.05815 [hep-th]].

[7] H. Sonoda and H. Suzuki, Derivation of a gradient flow from the exact

renormalization group, PTEP 2019 no. 3, (2019) 033B05 [arXiv:1901.05169

[hep-th]].

[8] H. Sonoda and H. Suzuki, Gradient flow exact renormalization group, PTEP 2021

no. 2, (2021) 023B05 [arXiv:2012.03568 [hep-th]].

[9] Y. Miyakawa and H. Suzuki, Gradient flow exact renormalization group – inclusion

of fermion fields, arXiv:2106.11142 [hep-th].

[10] Y. Miyakawa, H. Sonoda, and H. Suzuki, Manifestly gauge invariant exact

renormalization group for quantum electrodynamics, arXiv:2111.15529 [hep-th].

[11] O. J. Rosten, Fundamentals of the Exact Renormalization Group, Phys. Rept. 511

(2012) 177–272 [arXiv:1003.1366 [hep-th]].

[12] H. Suzuki, Online iTHEMS Lecture on Gradient Flow Exact Renormalization

Group,.

73

[13] H. Sonoda, Equivalence of Wilson Actions, PTEP 2015 no. 10, (2015) 103B01

[arXiv:1503.08578 [hep-th]].

[14] J. Berges, N. Tetradis, and C. Wetterich, Nonperturbative renormalization flow in

quantum field theory and statistical physics, Phys. Rept. 363 (2002) 223–386

[arXiv:hep-ph/0005122].

[15] J. Polonyi, Lectures on the functional renormalization group method, Central Eur.

J. Phys. 1 (2003) 1–71 [arXiv:hep-th/0110026].

[16] J. M. Pawlowski, Aspects of the functional renormalisation group, Annals Phys.

322 (2007) 2831–2915 [arXiv:hep-th/0512261].

[17] H. Gies, Introduction to the functional RG and applications to gauge theories, Lect.

Notes Phys. 852 (2012) 287–348 [arXiv:hep-ph/0611146].

[18] S. R. Coleman and J. Mandula, All Possible Symmetries of the S Matrix, Phys.

Rev. 159 (1967) 1251–1256.

[19] A. B. Zamolodchikov, Irreversibility of the Flux of the Renormalization Group in a

2D Field Theory, JETP Lett. 43 (1986) 730–732.

[20] J. L. Cardy, Is There a c Theorem in Four-Dimensions?, Phys. Lett. B 215 (1988)

749–752.

[21] H. Osborn, Derivation of a Four-dimensional c Theorem, Phys. Lett. B 222 (1989)

97–102.

[22] Z. Komargodski and A. Schwimmer, On Renormalization Group Flows in Four

Dimensions, JHEP 12 (2011) 099 [arXiv:1107.3987 [hep-th]].

[23] K. G. Wilson and M. E. Fisher, Critical exponents in 3.99 dimensions, Phys. Rev.

Lett. 28 (1972) 240–243.

[24] H. Makino, O. Morikawa, and H. Suzuki, Gradient flow and the Wilsonian

renormalization group flow, PTEP 2018 no. 5, (2018) 053B02 [arXiv:1802.07897

[hep-th]].

[25] Y. Miyakawa, Axial anomaly in the gradient flow exact renormalization group,

arXiv:2201.08181 [hep-th].

[26] H. Sonoda and H. Suzuki, One-particle irreducible Wilson action in the gradient

flow exact renormalization group formalism, PTEP 2022 no. 5, (2022) 053B01

[arXiv:2201.04448 [hep-th]].

[27] M. Luscher, Trivializing maps, the Wilson flow and the HMC algorithm, Commun.

Math. Phys. 293 (2010) 899–919 [arXiv:0907.5491 [hep-lat]].

74

[28] M. L¨

uscher, Properties and uses of the Wilson flow in lattice QCD, JHEP 08

(2010) 071 [arXiv:1006.4518 [hep-lat]]. [Erratum: JHEP 03, 092 (2014)].

[29] M. Luscher and P. Weisz, Perturbative analysis of the gradient flow in non-abelian

gauge theories, JHEP 02 (2011) 051 [arXiv:1101.0963 [hep-th]].

[30] M. Luscher, Chiral symmetry and the Yang–Mills gradient flow, JHEP 04 (2013)

123 [arXiv:1302.5246 [hep-lat]].

[31] M. L¨

uscher, Future applications of the Yang-Mills gradient flow in lattice QCD, PoS

LATTICE2013 (2014) 016 [arXiv:1308.5598 [hep-lat]].

[32] P. H. Ginsparg and K. G. Wilson, A Remnant of Chiral Symmetry on the Lattice,

Phys. Rev. D 25 (1982) 2649.

[33] S. L. Adler, Axial vector vertex in spinor electrodynamics, Phys. Rev. 177 (1969)

2426–2438.

[34] J. S. Bell and R. Jackiw, A PCAC puzzle: π 0 → γγ in the σ model, Nuovo Cim. A

60 (1969) 47–61.

[35] M. Matsumoto, G. Tanaka, and A. Tsuchiya, The renormalization group and the

diffusion equation, PTEP 2021 no. 2, (2021) 023B02 [arXiv:2011.14687 [hep-th]].

[36] H. Makino and H. Suzuki, Renormalizability of the gradient flow in the 2D O(N )

non-linear sigma model, PTEP 2015 no. 3, (2015) 033B08 [arXiv:1410.7538

[hep-lat]].

[37] S. Aoki, K. Kikuchi, and T. Onogi, Gradient Flow of O(N) nonlinear sigma model

at large N, JHEP 04 (2015) 156 [arXiv:1412.8249 [hep-th]].

[38] F. Capponi, A. Rago, L. Del Debbio, S. Ehret, and R. Pellegrini, Renormalisation

of the energy-momentum tensor in scalar field theory using the Wilson flow, PoS

LATTICE2015 (2016) 306 [arXiv:1512.02851 [hep-lat]].

[39] S. Dutta, B. Sathiapalan, and H. Sonoda, Wilson action for the O(N ) model, Nucl.

Phys. B 956 (2020) 115022 [arXiv:2003.02773 [hep-th]].

[40] M. Niedermaier and M. Reuter, The Asymptotic Safety Scenario in Quantum

Gravity, Living Rev. Rel. 9 (2006) 5–173.

[41] M. Reuter and F. Saueressig, Quantum Einstein Gravity, New J. Phys. 14 (2012)

055022 [arXiv:1202.2274 [hep-th]].

[42] J. Ambjorn, A. Goerlich, J. Jurkiewicz, and R. Loll, Nonperturbative Quantum

Gravity, Phys. Rept. 519 (2012) 127–210 [arXiv:1203.3591 [hep-th]].

75

[43] R. Percacci, Asymptotic Safety, arXiv:0709.3851 [hep-th].

[44] M. Niedermaier, The Asymptotic safety scenario in quantum gravity: An

Introduction, Class. Quant. Grav. 24 (2007) R171–230 [arXiv:gr-qc/0610018].

76

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