Abstract
We calculate the low-lying spectra of glueballs and confining flux tubes in the U(1) lattice gauge theory in 2 + 1 dimensions. We see that up to modest lattice spacing corrections, the glueball states are consistent with being multiparticle states composed of non-interacting massive JPC = 0− − particles. We observe that the ag2 → 0 limit is, as expected, unconventional, and follows the well-known saddle-point analysis of Polyakov to a good approximation. The spectrum of closed (winding) flux tubes exhibits the presence of a massive world-sheet excitation whose mass is consistent with that of the bulk screening mass. These U(1) calculations are intended to complement existing lattice calculations of the properties of SU(N ≥ 2) and SO(N ≥ 3) gauge theories in D = 2 + 1.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A.M. Polyakov, Compact gauge fields and the infrared catastrophe, Phys. Lett. B 59 (1975) 82 [INSPIRE].
A.M. Polyakov, Quark confinement and topology of gauge groups, Nucl. Phys. B 120 (1977) 429 [INSPIRE].
A. Polyakov, Gauge fields and strings, Harwood Academic Publishers, Reading U.S.A. (1987).
T. Banks, R. Myerson and J.B. Kogut, Phase transitions in Abelian lattice gauge theories, Nucl. Phys. B 129 (1977) 493 [INSPIRE].
M. Gopfert and G. Mack, Proof of confinement of static quarks in three-dimensional U(1) lattice gauge theory for all values of the coupling constant, Commun. Math. Phys. 82 (1981) 545 [INSPIRE].
M. Karliner and G. Mack, Mass gap and string tension in QED 3 comparison of theory with monte carlo simulation, Nucl. Phys. B 225 (1983) 371 [INSPIRE].
K.R. Ito, Upper and lower bound for the string tension in the three-dimensional lattice quantum electrodynamics, Nucl. Phys. B 205 (1982) 440 [Erratum ibid. B 215 (1983) 136] [INSPIRE].
M. Loan, M. Brunner, C. Sloggett and C. Hamer, Path integral Monte Carlo approach to the U(1) lattice gauge theory in (2 + 1)-dimensions, Phys. Rev. D 68 (2003) 034504 [hep-lat/0209159] [INSPIRE].
M.J. Teper, SU(N) gauge theories in (2 + 1)-dimensions, Phys. Rev. D 59 (1999) 014512 [hep-lat/9804008] [INSPIRE].
A. Athenodorou and M. Teper, SU(N) gauge theories in 2 + 1 dimensions: glueball spectra and k-string tensions, JHEP 02 (2017) 015 [arXiv:1609.03873] [INSPIRE].
R. Lau and M. Teper, SO(N) gauge theories in 2 + 1 dimensions: glueball spectra and confinement, JHEP 10 (2017) 022 [arXiv:1701.06941] [INSPIRE].
M. Caselle, M. Panero and D. Vadacchino, Width of the flux tube in compact U(1) gauge theory in three dimensions, JHEP 02 (2016) 180 [arXiv:1601.07455] [INSPIRE].
M. Caselle, M. Panero, R. Pellegrini and D. Vadacchino, A different kind of string, JHEP 01 (2015) 105 [arXiv:1406.5127] [INSPIRE].
M. Teper, An improved method for lattice glueball calculations, Phys. Lett. B 183 (1987) 345 [INSPIRE].
O. Aharony and Z. Komargodski, The Effective Theory of Long Strings, JHEP 05 (2013) 118 [arXiv:1302.6257] [INSPIRE].
O. Aharony and E. Karzbrun, On the effective action of confining strings, JHEP 06 (2009) 012 [arXiv:0903.1927] [INSPIRE].
S. Dubovsky, R. Flauger and V. Gorbenko, Effective String Theory Revisited, JHEP 09 (2012) 044 [arXiv:1203.1054] [INSPIRE].
M. Lüscher and P. Weisz, String excitation energies in SU(N) gauge theories beyond the free-string approximation, JHEP 07 (2004) 014 [hep-th/0406205] [INSPIRE].
A. Athenodorou and M. Teper, Closed flux tubes in D = 2 + 1 SU(N) gauge theories: dynamics and effective string description, JHEP 10 (2016) 093 [arXiv:1602.07634] [INSPIRE].
A. Athenodorou and M. Teper, Closed flux tubes in higher representations and their string description in D = 2 + 1 SU(N) gauge theories, JHEP 06 (2013) 053 [arXiv:1303.5946] [INSPIRE].
A. Athenodorou, B. Bringoltz and M. Teper, Closed flux tubes and their string description in D = 2 + 1 SU(N) gauge theories, JHEP 05 (2011) 042 [arXiv:1103.5854] [INSPIRE].
E. Seiler, Upper Bound on the Color Confining Potential, Phys. Rev. D 18 (1978) 482 [INSPIRE].
T. Copeland, Monopoles and Confinement in U(1) Lattice Gauge Theory, Ph.D. Thesis, Oxford University, Oxford U.K. (1990).
R. Wensley, Monopoles And U(1) Lattice Gauge Theory, Ph.D Thesis, University of Illinois, Chicago U.S.A. (1989), preprint ILL-TH-89-25.
R.J. Wensley and J.D. Stack, Monopoles and Confinement in Three-dimensions, Phys. Rev. Lett. 63 (1989) 1764 [INSPIRE].
P.A.M. Dirac, Quantised singularities in the electromagnetic field, Proc. Roy. Soc. Lond. A 133 (1931) 60 [INSPIRE].
T.A. DeGrand and D. Toussaint, Topological Excitations and Monte Carlo Simulation of Abelian Gauge Theory, Phys. Rev. D 22 (1980) 2478 [INSPIRE].
J. Villain, Theory of one- and two-dimensional magnets with an easy magnetization plane. II. The planar, classical, two-dimensional magnet, J. Phys. France 36 (1975) 581.
Z. Schram and M. Teper, Identifying monopoles on a lattice, Phys. Rev. D 48 (1993) 2881 [INSPIRE].
B. Svetitsky and L.G. Yaffe, Critical Behavior at Finite Temperature Confinement Transitions, Nucl. Phys. B 210 (1982) 423 [INSPIRE].
J.M. Kosterlitz and D.J. Thouless, Ordering, metastability and phase transitions in two-dimensional systems, J. Phys. C 6 (1973) 1181 [INSPIRE].
O. Borisenko, V. Chelnokov, M. Gravina and A. Papa, Deconfinement and universality in the 3D U(1) lattice gauge theory at finite temperature: study in the dual formulation, JHEP 09 (2015) 062 [arXiv:1507.00833] [INSPIRE].
M.N. Chernodub, E.-M. Ilgenfritz and A. Schiller, A Lattice study of 3 − D compact QED at finite temperature, Phys. Rev. D 64 (2001) 054507 [hep-lat/0105021] [INSPIRE].
P.D. Coddington, A.J.G. Hey, A.A. Middleton and J.S. Townsend, The Deconfining Transition for Finite Temperature U(1) Lattice Gauge Theory in (2+1)-dimensions, Phys. Lett. B 175 (1986) 64 [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].
S. Dubovsky, R. Flauger and V. Gorbenko, Solving the Simplest Theory of Quantum Gravity, JHEP 09 (2012) 133 [arXiv:1205.6805] [INSPIRE].
S. Dubovsky and V. Gorbenko, Towards a Theory of the QCD String, JHEP 02 (2016) 022 [arXiv:1511.01908] [INSPIRE].
S. Dubovsky, R. Flauger and V. Gorbenko, Evidence from Lattice Data for a New Particle on the Worldsheet of the QCD Flux Tube, Phys. Rev. Lett. 111 (2013) 062006 [arXiv:1301.2325] [INSPIRE].
A. Athenodorou and M. Teper, On the mass of the world-sheet ’axion’ in SU(N) gauge theories in 3 + 1 dimensions, Phys. Lett. B 771 (2017) 408 [arXiv:1702.03717] [INSPIRE].
A. Athenodorou, B. Bringoltz and M. Teper, Closed flux tubes and their string description in D = 3 + 1 SU(N) gauge theories, JHEP 02 (2011) 030 [arXiv:1007.4720] [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: 1811.06280
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, 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 licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Athenodorou, A., Teper, M. On the spectrum and string tension of U(1) lattice gauge theory in 2 + 1 dimensions. J. High Energ. Phys. 2019, 63 (2019). https://doi.org/10.1007/JHEP01(2019)063
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2019)063