Abstract
We numerically explore an alternative discretization of continuum SU(Nc) Yang-Mills theory on a Euclidean spacetime lattice, originally introduced by Budzcies and Zirnbauer for gauge group U(Nc). This discretization can be reformulated such that the self-interactions of the gauge field are induced by a path integral over Nb auxiliary bosonic fields, which couple linearly to the gauge field. In the first paper of the series we have shown that the theory reproduces continuum SU(Nc) Yang-Mills theory in d = 2 dimensions if Nb is larger than Nc − \( \frac{3}{4} \) and conjectured, following the argument of Budzcies and Zirnbauer, that this remains true for d > 2. In the present paper, we test this conjecture by performing lattice simulations of the simplest nontrivial case, i.e., gauge group SU(2) in three dimensions. We show that observables computed in the induced theory, such as the static q\( \overline{q} \) potential and the deconfinement transition temperature, agree with the same observables computed from the ordinary plaquette action up to lattice artifacts. We also find evidence that the bound for Nb can be relaxed to Nc − \( \frac{5}{4} \) as conjectured in our earlier paper. Studies of how the new discretization can be used to change the order of integration in the path integral to arrive at dual formulations of QCD are left for future work.
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References
J.M. Blairon, R. Brout, F. Englert and J. Greensite, Chiral Symmetry Breaking in the Action Formulation of Lattice Gauge Theory, Nucl. Phys.B 180 (1981) 439 [INSPIRE].
H. Kluberg-Stern, A. Morel, O. Napoly and B. Petersson, Spontaneous Chiral Symmetry Breaking for a U(N) Gauge Theory on a Lattice, Nucl. Phys.B 190 (1981) 504 [INSPIRE].
N. Kawamoto and J. Smit, Effective Lagrangian and Dynamical Symmetry Breaking in Strongly Coupled Lattice QCD, Nucl. Phys.B 192 (1981) 100 [INSPIRE].
P. Rossi and U. Wolff, Lattice QCD With Fermions at Strong Coupling: A Dimer System, Nucl. Phys.B 248 (1984) 105 [INSPIRE].
F. Karsch and K.H. Mutter, Strong coupling QCD at finite baryon number density, Nucl. Phys.B 313 (1989) 541 [INSPIRE].
M. Bander, Equivalence of Lattice Gauge and Spin Theories, Phys. Lett.126B (1983) 463 [INSPIRE].
H.W. Hamber, Lattice gauge theories at large N (f), Phys. Lett.126B (1983) 471 [INSPIRE].
V.A. Kazakov and A.A. Migdal, Induced QCD at large N, Nucl. Phys.B 397 (1993) 214 [hep-th/9206015] [INSPIRE].
A. Hasenfratz and P. Hasenfratz, The Equivalence of the SU(N) Yang-Mills theory with a purely fermionic model, Phys. Lett.B 297 (1992) 166 [hep-lat/9207017] [INSPIRE].
J. Budczies and M.R. Zirnbauer, Howe duality for an induced model of lattice U(N) Yang-Mills theory, math-ph/0305058 [INSPIRE].
B.B. Brandt, R. Lohmayer and T. Wettig, Induced QCD I: Theory, JHEP11 (2016) 087 [arXiv:1609.06466] [INSPIRE].
R. Sommer, A New way to set the energy scale in lattice gauge theories and its applications to the static force and α sin SU(2) Yang-Mills theory, Nucl. Phys.B 411 (1994) 839 [hep-lat/9310022] [INSPIRE].
H. Vairinhos and P. de Forcrand, Lattice gauge theory without link variables, JHEP12 (2014) 038 [arXiv:1409.8442] [INSPIRE].
B.B. Brandt and T. Wettig, Induced QCD with two auxiliary bosonic fields, PoS(LATTICE2014) 307 (2015) [arXiv:1411.3350] [INSPIRE].
B.B. Brandt, R. Lohmayer and T. Wettig, Induced YM Theory with Auxiliary Bosons, PoS(LATTICE2015) 276 (2016) [arXiv:1511.08374] [INSPIRE].
K.G. Wilson, Confinement of Quarks, Phys. Rev.D 10 (1974) 2445 [INSPIRE].
A.D. Kennedy and B.J. Pendleton, Improved Heat Bath Method for Monte Carlo Calculations in Lattice Gauge Theories, Phys. Lett.156B (1985) 393 [INSPIRE].
M. Creutz, Overrelaxation and Monte Carlo Simulation, Phys. Rev.D 36 (1987) 515 [INSPIRE].
N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller and E. Teller, Equation of state calculations by fast computing machines, J. Chem. Phys.21 (1953) 1087 [INSPIRE].
P. Majumdar, Continuum limit of the spectrum of the hadronic string, hep-lat/0406037 [INSPIRE].
N.D. Hari Dass and P. Majumdar, Continuum limit of string formation in 3-D SU(2) LGT, Phys. Lett.B 658 (2008) 273 [hep-lat/0702019] [INSPIRE].
B.B. Brandt and P. Majumdar, Spectrum of the QCD flux tube in 3d SU(2) lattice gauge theory, Phys. Lett.B 682 (2009) 253 [arXiv:0905.4195] [INSPIRE].
B.B. Brandt, Probing boundary-corrections to Nambu-Goto open string energy levels in 3d SU(2) gauge theory, JHEP02 (2011) 040 [arXiv:1010.3625] [INSPIRE].
B.B. Brandt, Spectrum of the open QCD flux tube in d = 2 + 1 and its effective string description, PoS(EPS-HEP2013) 540 (2013) [arXiv:1308.4993] [INSPIRE].
B.B. Brandt, Spectrum of the open QCD flux tube and its effective string description I: 3d static potential in SU(N = 2, 3), JHEP07 (2017) 008 [arXiv:1705.03828] [INSPIRE].
B.B. Brandt, Spectrum of the open QCD flux tube and its effective string description, in 13th Conference on Quark Confinement and the Hadron Spectrum (Confinement XIII), Maynooth, Ireland, July 31-August 6, 2018 (2018) [arXiv:1811.11779] [INSPIRE].
B.B. Brandt and M. Meineri, Effective string description of confining flux tubes, Int. J. Mod. Phys.A 31 (2016) 1643001 [arXiv:1603.06969] [INSPIRE].
O. Aharony and Z. Komargodski, The Effective Theory of Long Strings, JHEP05 (2013) 118 [arXiv:1302.6257] [INSPIRE].
J.F. Arvis, The Exact q \( \overline{q} \)Potential in Nambu String Theory, Phys. Lett.127B (1983) 106 [INSPIRE].
O. Aharony and N. Klinghoffer, Corrections to Nambu-Goto energy levels from the effective string action, JHEP12 (2010) 058 [arXiv:1008.2648] [INSPIRE].
O. Aharony, M. Field and N. Klinghoffer, The effective string spectrum in the orthogonal gauge, JHEP04 (2012) 048 [arXiv:1111.5757] [INSPIRE].
S. Dubovsky, R. Flauger and V. Gorbenko, Effective String Theory Revisited, JHEP09 (2012) 044 [arXiv:1203.1054] [INSPIRE].
S. Dubovsky, R. Flauger and V. Gorbenko, Flux Tube Spectra from Approximate Integrability at Low Energies, J. Exp. Theor. Phys.120 (2015) 399 [arXiv:1404.0037] [INSPIRE].
A.M. Polyakov, Confining strings, Nucl. Phys.B 486 (1997) 23 [hep-th/9607049] [INSPIRE].
H. Panagopoulos, A. Skouroupathis and A. Tsapalis, Free energy and plaquette expectation value for gluons on the lattice, in three dimensions, Phys. Rev.D 73 (2006) 054511 [hep-lat/0601009] [INSPIRE].
J. Engels et al., A Study of finite temperature gauge theory in (2 + 1)-dimensions, Nucl. Phys. Proc. Suppl.53 (1997) 420 [hep-lat/9608099] [INSPIRE].
F.Y. Wu, The Potts model, Rev. Mod. Phys.54 (1982) 235 [Erratum ibid.55 (1983) 315] [INSPIRE].
J. Liddle and M. Teper, The Deconfining phase transition in D = 2 + 1 SU(N) gauge theories, arXiv:0803.2128 [INSPIRE].
J. Engels, J. Fingberg and V.K. Mitrjushkin, Efficient calculation of critical parameters in SU(2) gauge theory, Phys. Lett.B 298 (1993) 154 [INSPIRE].
A.M. Ferrenberg and R.H. Swendsen, New Monte Carlo Technique for Studying Phase Transitions, Phys. Rev. Lett.61 (1988) 2635 [INSPIRE].
S. Duane, A.D. Kennedy, B.J. Pendleton and D. Roweth, Hybrid Monte Carlo, Phys. Lett.B 195 (1987) 216 [INSPIRE].
M. Lüscher and P. Weisz, Locality and exponential error reduction in numerical lattice gauge theory, JHEP09 (2001) 010 [hep-lat/0108014] [INSPIRE].
P. Majumdar, Experiences with the multilevel algorithm, Nucl. Phys. Proc. Suppl.119 (2003) 1021 [hep-lat/0208068] [INSPIRE].
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Brandt, B.B., Lohmayer, R. & Wettig, T. Induced QCD II: numerical results. J. High Energ. Phys. 2019, 43 (2019). https://doi.org/10.1007/JHEP07(2019)043
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DOI: https://doi.org/10.1007/JHEP07(2019)043