The lattice gradient flow at tree-level and its improvement

Journal of High Energy Physics

Volumn 2014, Issue 9, 2014, Pages 1-16

  Fodor, Zoltan ^a,b,c   Holland, Kieran ^d,e   Kuti, Julius ^f   Mondal, Santanu ^c   Nogradi, Daniel ^c   Wong, Chik Him ^f  

^a UNIVERSITY OF WUPPERTAL   (Germany)

^b FORSCHUNGSZENTRUM JÜLICH   (Germany)

^c EÖTVÖS LORÁND UNIVERSITY   (Hungary)

^d UNIVERSITY OF THE PACIFIC   (United States)

^e UNIVERSITY OF BERN   (Switzerland)

^f UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Lattice Gauge Field Theories; Lattice Quantum Field Theory

Indexed keywords

EID: 84914156476     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1007/JHEP09(2014)018     Document Type: Article

References (29)

1. M. Lüscher, Trivializing maps, the Wilson flow and the HMC algorithm, Commun. Math. Phys.293 (2010) 899 [arXiv:0907.5491] [INSPIRE].
2. M. Lüscher, Properties and uses of the Wilson flow in lattice QCD, JHEP08 (2010) 071 [arXiv:1006.4518] [INSPIRE].
3. M. Lüscher, Topology, the Wilson flow and the HMC algorithm, PoS(LATTICE 2010)015 [arXiv:1009.5877] [INSPIRE].
4. M. Lüscher and P. Weisz, Perturbative analysis of the gradient flow in non-Abelian gauge theories, JHEP02 (2011) 051 [arXiv:1101.0963] [INSPIRE].
5. S. Borsányi et al., High-precision scale setting in lattice QCD, JHEP09 (2012) 010 [arXiv:1203.4469] [INSPIRE].
6. MILC collaboration, A. Bazavov et al., Symanzik flow on HISQ ensembles, arXiv:1311.1474 [INSPIRE].
7. R. Sommer, Scale setting in lattice QCD, PoS(LATTICE 2013)015 [arXiv:1401.3270] [INSPIRE].
8. Z. Fodor, K. Holland, J. Kuti, D. Nogradi and C.H. Wong, The Yang-Mills gradient flow in finite volume, JHEP11 (2012) 007 [arXiv:1208.1051] [INSPIRE].
9. Z. Fodor, K. Holland, J. Kuti, D. Nogradi and C.H. Wong, The gradient flow running coupling scheme, PoS(LATTICE 2012)050 [arXiv:1211.3247] [INSPIRE].
10. P. Fritzsch and A. Ramos, The gradient flow coupling in the Schrödinger functional, JHEP10 (2013) 008 [arXiv:1301.4388] [INSPIRE].
11. P. Fritzsch and A. Ramos, Studying the gradient flow coupling in the Schrödinger functional, PoS(LATTICE 2013)319 [arXiv:1308.4559] [INSPIRE].
12. A. Ramos, The gradient flow in a twisted box, PoS(LATTICE 2013)053 [arXiv:1308.4558] [INSPIRE].
13. P. Fritzsch, A. Ramos and F. Stollenwerk, Critical slowing down and the gradient flow coupling in the Schrödinger functional, PoS(LATTICE 2013)461 [arXiv:1311.7304] [INSPIRE].
14. J. Rantaharju, The gradient flow coupling in minimal walking technicolor, PoS(LATTICE 2013)084 [arXiv:1311.3719] [INSPIRE].
15. M. Lüscher, Step scaling and the Yang-Mills gradient flow, JHEP06 (2014) 105 [arXiv:1404.5930] [INSPIRE].
16. FlowQCD collaboration, M. Asakawa, T. Hatsuda, E. Itou, M. Kitazawa and H. Suzuki, Thermodynamics of SU(3) gauge theory from gradient flow, Phys. Rev.D 90 (2014) 011501 [arXiv:1312.7492] [INSPIRE].
17. O. Bär and M. Golterman, Chiral perturbation theory for gradient flow observables, Phys. Rev.D 89 (2014) 034505 [arXiv:1312.4999] [INSPIRE].
18. H. Suzuki, Energy-momentum tensor from the Yang-Mills gradient flow, Prog. Theor. Exp. Phys.2013 (2013) 083B03 [arXiv:1304.0533] [INSPIRE].
19. L. Del Debbio, A. Patella and A. Rago, Space-time symmetries and the Yang-Mills gradient flow, JHEP11 (2013) 212 [arXiv:1306.1173] [INSPIRE].
20. H. Makino and H. Suzuki, Lattice energy-momentum tensor from the Yang-Mills gradient flow-inclusion of fermion fields, Prog. Theor. Exp. Phys.2014 (2014) 063B02 [arXiv:1403.4772] [INSPIRE].
21. M. Lüscher, Chiral symmetry and the Yang-Mills gradient flow, JHEP04 (2013) 123 [arXiv:1302.5246] [INSPIRE].
22. A. Shindler, Chiral Ward identities, automatic O(a) improvement and the gradient flow, Nucl. Phys.B 881 (2014) 71 [arXiv:1312.4908] [INSPIRE].
23. A. Cheng, A. Hasenfratz, Y. Liu, G. Petropoulos and D. Schaich, Improving the continuum limit of gradient flow step scaling, JHEP05 (2014) 137 [arXiv:1404.0984] [INSPIRE].
24. P. Weisz, Continuum limit improved lattice action for pure Yang-Mills theory. 1, Nucl. Phys.B 212 (1983) 1 [INSPIRE].
25. K. Symanzik, Continuum limit and improved action in lattice theories. 1. Principles and ϕ4theory, Nucl. Phys.B 226 (1983) 187 [INSPIRE].
26. P. Weisz and R. Wohlert, Continuum limit improved lattice action for pure Yang-Mills theory. 2, Nucl. Phys.B 236 (1984) 397 [Erratum ibid.B 247 (1984) 544] [INSPIRE].
27. M. Lüscher and P. Weisz, On-shell improved lattice gauge theories, Commun. Math. Phys.97 (1985) 59 [Erratum ibid.98 (1985) 433] [INSPIRE].
28. M. Lüscher and P. Weisz, Computation of the action for on-shell improved lattice gauge theories at weak coupling, Phys. Lett.B 158 (1985) 250 [INSPIRE].
29. A. Coste, A. Gonzalez-Arroyo, J. Jurkiewicz and C.P. Korthals Altes, Zero momentum contribution to Wilson loops in periodic boxes, Nucl. Phys.B 262 (1985) 67 [INSPIRE].