Abstract
We find that using open boundary condition in the temporal direction can yield the expected value of the topological susceptibility in lattice SU(3) Yang-Mills theory. As a further check, we show that the result agrees with numerical simulations employing the periodic boundary condition. Our results support the preferability of the open boundary condition over the periodic boundary condition as the former allows for computation at smaller lattice spacings needed for continuum extrapolation at a lower computational cost.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
M. Lüscher, Topology, the Wilson flow and the HMC algorithm, PoS (LATTICE 2010) 015 [arXiv:1009.5877] [INSPIRE].
M. Lüscher and S. Schaefer, Lattice QCD without topology barriers, JHEP 07 (2011) 036 [arXiv:1105.4749] [INSPIRE].
M. Lüscher and S. Schaefer, Lattice QCD with open boundary conditions and twisted-mass reweighting, Comput. Phys. Commun. 184 (2013) 519 [arXiv:1206.2809] [INSPIRE].
M. Grady, Connecting phase transitions between the 3D O(4) Heisenberg model and 4D SU(2) lattice gauge theory, arXiv:1104.3331 [INSPIRE].
E. Witten, Current algebra theorems for the U(1) Goldstone boson, Nucl. Phys. B 156 (1979) 269 [INSPIRE].
G. Veneziano, U(1) without instantons, Nucl. Phys. B 159 (1979) 213 [INSPIRE].
E. Seiler, Some more remarks on the Witten-Veneziano formula for the eta-prime mass, Phys. Lett. B 525 (2002) 355 [hep-th/0111125] [INSPIRE].
L. Del Debbio, L. Giusti and C. Pica, Topological susceptibility in the SU(3) gauge theory, Phys. Rev. Lett. 94 (2005) 032003 [hep-th/0407052] [INSPIRE].
S. Dürr, Z. Fodor, C. Hölbling and T. Kurth, Precision study of the SU(3) topological susceptibility in the continuum, JHEP 04 (2007) 055 [hep-lat/0612021] [INSPIRE].
M. Lüscher and F. Palombi, Universality of the topological susceptibility in the SU(3) gauge theory, JHEP 09 (2010) 110 [arXiv:1008.0732] [INSPIRE].
M. Lüscher, Topological effects in QCD and the problem of short distance singularities, Phys. Lett. B 593 (2004) 296 [hep-th/0404034] [INSPIRE].
L. Giusti and M. Lüscher, Chiral symmetry breaking and the Banks-Casher relation in lattice QCD with Wilson quarks, JHEP 03 (2009) 013 [arXiv:0812.3638] [INSPIRE].
H. Asakawa and M. Suzuki, Boundary susceptibilities of the Hubbard model in open chains, J. Phys. A 29 (1996) 7811.
ALPHA collaboration, M. Guagnelli, R. Sommer and H. Wittig, Precision computation of a low-energy reference scale in quenched lattice QCD, Nucl. Phys. B 535 (1998) 389 [hep-lat/9806005] [INSPIRE].
S. Necco and R. Sommer, The N f = 0 heavy quark potential from short to intermediate distances, Nucl. Phys. B 622 (2002) 328 [hep-lat/0108008] [INSPIRE].
M. Lüscher, Trivializing maps, the Wilson flow and the HMC algorithm, Commun. Math. Phys. 293 (2010) 899 [arXiv:0907.5491] [INSPIRE].
M. Lüscher, Properties and uses of the Wilson flow in lattice QCD, JHEP 08 (2010) 071 [arXiv:1006.4518] [INSPIRE].
M. Lüscher and P. Weisz, Perturbative analysis of the gradient flow in non-abelian gauge theories, JHEP 02 (2011) 051 [arXiv:1101.0963] [INSPIRE].
S. Borsányi et al., High-precision scale setting in lattice QCD, JHEP 09 (2012) 010 [arXiv:1203.4469] [INSPIRE].
P. de Forcrand et al., Local topological and chiral properties of QCD, Nucl. Phys. Proc. Suppl. 73 (1999) 578 [hep-lat/9810033] [INSPIRE].
G. McGlynn and R.D. Mawhinney, Scaling, topological tunneling and actions for weak coupling DWF calculations, arXiv:1311.3695 [INSPIRE].
A. Chowdhury, A.K. De, A. Harindranath, J. Maiti and S. Mondal, Topological charge density correlator in lattice QCD with two flavours of unimproved Wilson fermions, JHEP 11 (2012) 029 [arXiv:1208.4235] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1311.6599
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Chowdhury, A., Harindranath, A., Maiti, J. et al. Topological susceptibility in lattice Yang-Mills theory with open boundary condition. J. High Energ. Phys. 2014, 45 (2014). https://doi.org/10.1007/JHEP02(2014)045
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2014)045