- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Larger physical volume and bounds on the number of matter fields in noncompact gauge theories on a lattice

F. Palumbo*

  • *Contact author: fabrizio.palumbo@lnf.infn.it
PDF

Phys. Rev. D 114, 074508 – Published 13 October, 2026

DOI: https://doi.org/10.1103/dv9t-mj75

Abstract

The work was motivated by the numerical result that, in a pure SU(2) gauge theory, the ratio R of the effective noncompact and compact lattice spacing is larger than 1 and increases with decreasing gauge coupling, with the expectation that it should further increase extending the parameter space. This means that with a noncompact regularization, at a given number of lattice sites and comparable scaling, one can obtain a larger physical volume whose importance for the control of size effects has long been known. We confirm qualitatively results and expectation by a perturbative evaluation of the effective lattice spacing in an expansion in the Plank constant of noncompact pure SU(2) and Abelian gauge theories, but we find in addition that R reaches the maximum value of 2. Including matter fields, we find that R increases (still up to 2) or decreases depending on the difference between the number of scalar and spinor degrees of freedom, and there are bounds on such a difference.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (23)

  1. K. G. Wilson, Renormalization group and critical phenomena. I. Renormalization group and the Kadanoff scaling picture, Phys. Rev. B 4, 3174 (1971); Renormalization group and critical phenomena. II. Phase space cell analysis of critical behaviour, 4, 3184 (1971); S. Weinberg, in General Relativity: An Einstein Centenary Survey, edited by S. W. Hawking and W. Israel (Cambridge University Press, Cambridge, United Kingdom, 1979), p. 790; a short review on the subject can be found in D. F. Litim and F. Sannino, Asymptotic safety guaranteed J. High Energy Phys. 12 (2014) 178; A. D. Bond and D. F. Litim, More asymptotic safety guaranteed; Phys. Rev. D 97, 085008 (2018); A. V. Bednyakov and A. I. Mukhaeva, Asymptotic safety in the Litim-Sannino model at four loops, 109, 065030 (2024); T. Steudtner, Effective potential and vacuum stability in the Litim-Sannino model, J. High Energy Phys. 05 (2024) 149.
  2. A. Pelissetto and E. Vicari, Three-dimensional ferromagnetic CP(N−1) models, Phys. Rev. E 100, 22122 (2019); Multicomponent compact Abelian-Higgs lattice models, 100, 042134 (2019); Large-N behaviour of three-dimensional lattice CPN−1 models, J. Stat. Mech. (2020) P033209.
  3. O. I. Motrunich and A. Vishwanath, Comparative study of Higgs transition in one-component and two-components lattice superconductor models, arXiv:0805.1494; C. Bonati, A. Pelissetto, and E. Vicari, Lattice Abelian-Higgs model with noncompact gauge fields, Phys. Rev. B 103, 085104 (2021); C. Bonati and N. Francini, Noncompact lattice Higgs model with Abelian discrete gauge groups: Phase diagram and gauge symmetry enlargement, 107, 035106 (2023).
  4. J. Smiseth, E. Smorgav, F. S. Nogueira, J. Hove, and A. Sudbo, Phase structure of (2+1)-dimensional compact lattice gauge theories and the transition from Mott insulator to fractionalized insulators, Phys. Rev. B 67, 205104 (2003); C. Bonati, A. Pelissetto, and E. Vicari, Higher-charge three-dimensional compact lattice Abelian-Higgs models, Phys. Rev. E 102, 062151 (2020).
  5. A. B. Kuklov, M. Matsumoto, N. V. Prokof’ev, B. V. Svistunov, and M. Troyer, Deconfined criticality: Generic first-order transition in the SU(2) symmetry case, Phys. Rev. Lett. 101, 050405 (2008); S. Sachdev, H. D. Scammell, M. S. Scheurer, and G. Tarnopolsky, Gauge theories for cuprates near optimal doping, Phys. Rev. B 99, 054516 (2019); H. D. Scammell, K. Patekar, M. S. Scheurer, and S. Sachdev, Phases of SU(2) gauge theory with multiple adjoint Higgs fields in 2+1 dimensions, 101, 205124 (2020); C. Bonati, A. Franchi, A. Pelissetto, and E. Vicari, Three-dimensional lattice SU(Nc) gauge theories with multiflavor scalar fields in the adjoint representation, 104, 115166 (2021).
  6. S. Sachdev, Topological order, emergent gauge fields and Fermi surface reconstruction, Rep. Prog. Phys. 82, 014001 (2019).
  7. G. Di Carlo and R. Scimia, Numerical study of the scaling properties of SU(2) lattice gauge theory in Palumbo noncompact regularization, Phys. Rev. D 63, 094501 (2001).
  8. F. Palumbo, Noncompact gauge fields on a lattice, Phys. Lett. B 244, 55 (1990).
  9. K. G. Wilson, Confinement of quarks, Phys. Rev. D 10, 2445 (1974).
  10. D. K. Sinclair, Light hadron spectroscopy, Nucl. Phys. B, Proc. Suppl. 47, 112 (1996); R. Petronzio, Structure functions on the lattice, 83–84, 136 (2000); L. Lellouch, Light hadron weak matrix elements, 94, 142 (2001).
  11. Particle Data Group, Lattice quantum chromodynamics?, arXiv:hep-lat/0503016
  12. G. Di Carlo, F. Palumbo, and R. Scimia, Larger physical volume with a noncompact lattice regularization of SU(N) theories, Nucl. Phys. B, Proc. Suppl. 106–107, 823 (2002).
  13. G. Veneziano, U(1) without instantons, Nucl. Phys. B159, 213 (1979).
  14. F. Palumbo, M. I. Polikarpov, and A. I. Veselov, Confinement in noncompact non Abelian gauge theories on a lattice, Phys. Lett. B 297, 171 (2002).
  15. C. M. Becchi and F. Palumbo, Noncompact gauge theories on a lattice: Perturbative study of the scaling properties, Nucl. Phys. B388, 595 (1992).
  16. B. Borasoy, W. Kramer, and D. Schutte, Application of the Hamiltonian formulation of Palumbo’s new lattice Yang-Mills theory, Phys. Rev. D 53, 2599 (1996); B. Dickmann, D. Schutte, and H. Kroger, Hamiltonian formulation of Palumbo’s non compact lattice gauge theory, 49, 3589 (1994).
  17. F. Palumbo and R. Scimia, Non compact gauge fields on a lattice: SU(N) theories, Phys. Rev. D 65, 074509 (2002).
  18. C. M. Becchi and F. Palumbo, Compact and non compact gauge theories on a lattice, Phys. Rev. D 44, R946 (1991).
  19. V. Azcoiti, G. Di Carlo, and A. F. Grillo, New proposal for including dynamical fermions in lattice gauge theories: The compact-QED case, Phys. Rev. Lett. 65, 2239 (1990); V. Azcoiti, A. Cruz, G. Di Carlo, A. F. Grillo, and A. Vladikas, Simulating lattice fermions by microcanonically averaging out the nonlocal dependence of the fermionic action, Phys. Rev. D 43, 3487 (1991); V. Azcoiti, G. Di Carlo, and A. F. Grillo, A new approach to non-compact lattice QED with light fermions, Int. J. Mod. Phys. A A8, 4235 (1993); M. Baig, H. Fort, S. Kim, J. B. Kogut, and D. K. Sinclair, Logarithmic triviality of scalar quantum electrodynamics, Phys. Rev. D 48, R2385 (1993); M. Baig, H. Fort, J. B. Kogut, and S. Kim, Phases and triviality of scalar quantum electrodynamics, 51, 5216 (1995).
  20. J. B. Kogut and E. Dagotto, A supercomputer study of strongly coupled QED, Phys. Rev. Lett. 59, 617 (1987); E. Dagotto and J. B. Kogut, Study of compact QED with light fermions, Nucl. Phys. B295, 123 (1988); S. Kim, J. B. Kogut, and M.-P. Lombardo, On the triviality of textbook quantum electrodynamics, Phys. Lett. B 502, 345 (2001); Gauged Nambu–Jona-Lasinio studies of the triviality of quantum electrodynamics, Phys. Rev. D 65, 054015 (2002).
  21. D. Babusci and F. Palumbo, Modified Abelian and SU(2) Wilson theories on a lattice from a noncompact regularization, Phys. Rev. D 110, 094511 (2024).
  22. R. Jackiw, Functional evaluation of the effective potential, Phys. Rev. D 9, 1686 (1974); L. Dolan and R. Jackiw, Gauge-invariant signal for gauge-symmetry breaking, 9, 2904 (1974).
  23. N. K. Nielsen, On the gauge dependence of spontaneous symmetry breaking in gauge theories, Nucl. Phys. B101, 173 (1975); R. Fukuda and T. Kugo, Gauge invariance in the effective action and potential, Phys. Rev. D 13, 3469 (1976); L. J. R. Aitchison and C. M. Fraser, Gauge invariance and the effective potential, Ann. Phys. (N.Y.) 156, 1 (1984).

Outline

Information

Phys. Rev. D 114, 074508– Published 13 October, 2026
  • Received 24 May 2026
  • Accepted 18 September 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation