Searching for continuous phase transitions in 5D SU(2) lattice gauge theory. (English) Zbl 1521.81193
Summary: We study the phase diagram of 5-dimensional SU(2) Yang-Mills theory on the lattice. We consider two extensions of the fundamental plaquette Wilson action in the search for the continuous phase transition suggested by the \(4 + \epsilon\) expansion. The extensions correspond to new terms in the action: i) a unit size plaquette in the adjoint representation or ii) a two-unit sided square plaquette in the fundamental representation. We use Monte Carlo to sample the first and second derivative of the entropy near the confinement phase transition, with lattices up to \(12^5\). While we exclude the presence of a second order phase transition in the parameter space we sampled for model i), our data is not conclusive in some regions of the parameter space of model ii).
MSC:
| 81T25 | Quantum field theory on lattices |
| 81T17 | Renormalization group methods applied to problems in quantum field theory |
| 81R40 | Symmetry breaking in quantum theory |
| 83E15 | Kaluza-Klein and other higher-dimensional theories |
Keywords:
conformal field theory; field theories in higher dimensions; lattice quantum field theory; renormalization groupReferences:
| [1] | Wilson, KG; Kogut, JB, The Renormalization group and the ϵ-expansion, Phys. Rept., 12, 75 (1974) · doi:10.1016/0370-1573(74)90023-4 |
| [2] | D. Poland, S. Rychkov and A. Vichi, The conformal bootstrap: theory, numerical techniques, and applications, Rev. Mod. Phys.91 (2019) 015002. |
| [3] | M.E. Peskin, Critical point behavior of the Wilson loop, Phys. Lett. B94 (1980) 161 [INSPIRE]. |
| [4] | A.M. Polyakov, Interaction of Goldstone particles in two-Dimensions. Applications to ferromagnets and massive Yang-Mills fields, Phys. Lett. B59 (1975) 79 [INSPIRE]. |
| [5] | W.A. Bardeen, B.W. Lee and R.E. Shrock, Phase transition in the nonlinear σ model in 2 + ϵ dimensional continuum, Phys. Rev. D14 (1976) 985 [INSPIRE]. |
| [6] | I.Y. Arefeva, E.R. Nissimov and S.J. Pacheva, Bphzl renormalization of 1/N expansion and critical behavior of the three-dimensional chiral field, Commun. Math. Phys.71 (1980) 213 [INSPIRE]. |
| [7] | Eichhorn, A., An asymptotically safe guide to quantum gravity and matter, Front. Astron. Space Sci., 5, 47 (2019) · doi:10.3389/fspas.2018.00047 |
| [8] | H. Gies, Renormalizability of gauge theories in extra dimensions, Phys. Rev. D68 (2003) 085015 [hep-th/0305208] [INSPIRE]. |
| [9] | T.R. Morris, Renormalizable extra-dimensional models, JHEP01 (2005) 002 [hep-ph/0410142] [INSPIRE]. |
| [10] | F. De Cesare, L. Di Pietro and M. Serone, Five-dimensional CFTs from the ϵ-expansion, Phys. Rev. D104 (2021) 105015 [arXiv:2107.00342]. |
| [11] | P. Benetti Genolini, M. Honda, H.-C. Kim, D. Tong and C. Vafa, Evidence for a non-supersymmetric 5d CFT from deformations of 5d SU(2) SYM, JHEP05 (2020) 058 [arXiv:2001.00023] [INSPIRE]. · Zbl 1437.81040 |
| [12] | Bertolini, M.; Mignosa, F., Supersymmetry breaking deformations and phase transitions in five dimensions, JHEP, 10, 244 (2021) · Zbl 1476.81130 · doi:10.1007/JHEP10(2021)244 |
| [13] | M. Creutz, Confinement and the critical dimensionality of space-time, Phys. Rev. Lett.43 (1979) 553 [Erratum ibid.43 (1979) 890] [INSPIRE]. |
| [14] | H. Kawai, M. Nio and Y. Okamoto, On existence of nonrenormalizable field theory: Pure SU(2) lattice gauge theory in five-dimensions, Prog. Theor. Phys.88 (1992) 341 [INSPIRE]. |
| [15] | J. Nishimura, On existence of nontrivial fixed points in large N gauge theory in more than four-dimensions, Mod. Phys. Lett. A11 (1996) 3049 [hep-lat/9608119] [INSPIRE]. · Zbl 1041.81560 |
| [16] | S. Ejiri, J. Kubo and M. Murata, A study on the nonperturbative existence of Yang-Mills theories with large extra dimensions, Phys. Rev. D62 (2000) 105025 [hep-ph/0006217] [INSPIRE]. |
| [17] | S. Ejiri, S. Fujimoto and J. Kubo, Scaling laws and effective dimension in lattice SU(2) Yang-Mills theory with a compactified extra dimension, Phys. Rev. D66 (2002) 036002 [hep-lat/0204022] [INSPIRE]. |
| [18] | K. Farakos, P. de Forcrand, C.P. Korthals Altes, M. Laine and M. Vettorazzo, Finite temperature Z(N) phase transition with Kaluza-Klein gauge fields, Nucl. Phys. B655 (2003) 170 [hep-ph/0207343] [INSPIRE]. · Zbl 1009.81519 |
| [19] | de Forcrand, P.; Kurkela, A.; Panero, M., The phase diagram of Yang-Mills theory with a compact extra dimension, JHEP, 06, 050 (2010) · Zbl 1290.81061 · doi:10.1007/JHEP06(2010)050 |
| [20] | Del Debbio, L.; Kenway, RD; Lambrou, E.; Rinaldi, E., The transition to a layered phase in the anisotropic five-dimensional SU(2) Yang-Mills theory, Phys. Lett. B, 724, 133 (2013) · Zbl 1331.81227 · doi:10.1016/j.physletb.2013.05.062 |
| [21] | Knechtli, F.; Rinaldi, E., Extra-dimensional models on the lattice, Int. J. Mod. Phys. A, 31, 1643002 (2016) · Zbl 1345.81094 · doi:10.1142/S0217751X16430028 |
| [22] | T. Kanazawa and A. Yamamoto, Asymptotically free lattice gauge theory in five dimensions, Phys. Rev. D91 (2015) 074508 [arXiv:1411.4667] [INSPIRE]. |
| [23] | L. Velazquez and J.C. Castro-Palacio, Extended canonical Monte Carlo methods: improving accuracy of microcanonical calculations using a reweighting technique, Phys. Rev. E91 (2015) 033308 [arXiv:1602.07045]. |
| [24] | Bonati, C.; D’Elia, M.; Martinelli, G.; Negro, F.; Sanfilippo, F.; Todaro, A., Topology in full QCD at high temperature: a multicanonical approach, JHEP, 11, 170 (2018) · Zbl 1404.81282 · doi:10.1007/JHEP11(2018)170 |
| [25] | J. Viana Lopes, M.D. Costa, J.M.B. Lopes dos Santos and R. Toral, Optimized multicanonical simulations: a proposal based on classical fluctuation theory, Phys. Rev. E74 (2006) 046702. |
| [26] | B.A. Berg and T. Neuhaus, Multicanonical ensemble: a new approach to simulate first order phase transitions, Phys. Rev. Lett.68 (1992) 9 [hep-lat/9202004] [INSPIRE]. |
| [27] | J. Lee, A New Monte Carlo algorithm: Entropic sampling, Phys. Rev. Lett.71 (1993) 211 [Erratum ibid.71 (1993) 2353] [INSPIRE]. |
| [28] | A.M. Ferrenberg and R.H. Swendsen, Optimized Monte Carlo analysis, Phys. Rev. Lett.63 (1989) 1195 [INSPIRE]. |
| [29] | Cardy, JL, Scaling and renormalization in statistical physics (1996), Cambridge U.K.: Cambridge University Press, Cambridge U.K. · doi:10.1017/CBO9781316036440 |
| [30] | L. Li and Y. Meurice, Lattice gluodynamics at negative g^2, Phys. Rev. D71 (2005) 016008 [hep-lat/0410029] [INSPIRE]. |
| [31] | M. Baig, Monte Carlo analysis of the SO(3) lattice gauge theory and the critical dimensionality of space-time, Phys. Rev. Lett.54 (1985) 167 [INSPIRE]. |
| [32] | M. Creutz, Quarks, gluons and lattices, Cambridge Monographs on Mathematical Physics. Cambridge University Press, Cambridge, U.K. (1985). |
| [33] | M. Creutz, Asymptotic freedom scales, Phys. Rev. Lett.45 (1980) 313 [INSPIRE]. |
| [34] | Gattringer, C.; Lang, CB, Quantum chromodynamics on the lattice (2010), Germany: Springer, Germany · doi:10.1007/978-3-642-01850-3 |
| [35] | Martino, L., A review of multiple try mcmc algorithms for signal processing, Dig. Signal Proc., 75, 134 (2018) · doi:10.1016/j.dsp.2018.01.004 |
| [36] | Hukushima, K.; Takayama, H.; Nemoto, K., Application of an extended ensemble method to spin glasses, Int. J. Mod. Phys. C, 07, 337 (1996) · doi:10.1142/S0129183196000272 |
| [37] | M. Creutz, Monte Carlo study of quantized SU(2) gauge theory, Phys. Rev. D21 (1980) 2308 [INSPIRE]. |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
