Abstract
We study fractional-derivative Maxwell theory, as appears in effective descriptions of, for example, large Nf QED3, graphene, and some types of surface defects. We argue that when the theory is realized on a lattice, monopole condensation leads to a confining phase via the Polyakov confinement mechanism.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
T. Appelquist and R.D. Pisarski, High-Temperature Yang-Mills Theories and Three-Dimensional Quantum Chromodynamics, Phys. Rev. D 23 (1981) 2305 [INSPIRE].
T. Appelquist, D. Nash and L.C.R. Wijewardhana, Critical Behavior in (2+1)-Dimensional QED, Phys. Rev. Lett. 60 (1988) 2575 [INSPIRE].
D. Anselmi, Large N expansion, conformal field theory and renormalization group flows in three-dimensions, JHEP 06 (2000) 042 [hep-th/0005261] [INSPIRE].
V. Borokhov, A. Kapustin and X.-K. Wu, Topological disorder operators in three-dimensional conformal field theory, JHEP 11 (2002) 049 [hep-th/0206054] [INSPIRE].
E. Witten, SL(2,Z) action on three-dimensional conformal field theories with Abelian symmetry, in the proceedings of the From Fields to Strings: Circumnavigating Theoretical Physics: A Conference in Tribute to Ian Kogan, (2003), p. 1173–1200 [hep-th/0307041] [INSPIRE].
S. Giombi, I.R. Klebanov and G. Tarnopolsky, Conformal QEDd, F-Theorem and the ϵ Expansion, J. Phys. A 49 (2016) 135403 [arXiv:1508.06354] [INSPIRE].
S.M. Chester and S.S. Pufu, Anomalous dimensions of scalar operators in QED3, JHEP 08 (2016) 069 [arXiv:1603.05582] [INSPIRE].
S. Giombi, G. Tarnopolsky and I.R. Klebanov, On CJ and CT in Conformal QED, JHEP 08 (2016) 156 [arXiv:1602.01076] [INSPIRE].
M. Dedushenko, Gluing. Part I. Integrals and symmetries, JHEP 04 (2020) 175 [arXiv:1807.04274] [INSPIRE].
J.M. Maldacena, The Large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [hep-th/9711200] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
M.A. Vasiliev, Consistent equation for interacting gauge fields of all spins in (3+1)-dimensions, Phys. Lett. B 243 (1990) 378 [INSPIRE].
I.R. Klebanov and A.M. Polyakov, AdS dual of the critical O(N) vector model, Phys. Lett. B 550 (2002) 213 [hep-th/0210114] [INSPIRE].
S. Giombi and X. Yin, The Higher Spin/Vector Model Duality, J. Phys. A 46 (2013) 214003 [arXiv:1208.4036] [INSPIRE].
S. Giombi et al., AdS Description of Induced Higher-Spin Gauge Theory, JHEP 10 (2013) 016 [arXiv:1306.5242] [INSPIRE].
M.F. Paulos, S. Rychkov, B.C. van Rees and B. Zan, Conformal Invariance in the Long-Range Ising Model, Nucl. Phys. B 902 (2016) 246 [arXiv:1509.00008] [INSPIRE].
C.P. Herzog and K.-W. Huang, Boundary Conformal Field Theory and a Boundary Central Charge, JHEP 10 (2017) 189 [arXiv:1707.06224] [INSPIRE].
S. Giombi and H. Khanchandani, O(N) models with boundary interactions and their long range generalizations, JHEP 08 (2020) 010 [arXiv:1912.08169] [INSPIRE].
A.O. Caldeira and A.J. Leggett, Influence of dissipation on quantum tunneling in macroscopic systems, Phys. Rev. Lett. 46 (1981) 211 [INSPIRE].
C.G. Callan Jr. and L. Thorlacius, Open string theory as dissipative quantum mechanics, Nucl. Phys. B 329 (1990) 117 [INSPIRE].
C.G. Callan, I.R. Klebanov, A.W.W. Ludwig and J.M. Maldacena, Exact solution of a boundary conformal field theory, Nucl. Phys. B 422 (1994) 417 [hep-th/9402113] [INSPIRE].
E.C. Marino, Quantum electrodynamics of particles on a plane and the Chern-Simons theory, Nucl. Phys. B 408 (1993) 551 [hep-th/9301034] [INSPIRE].
S. Teber, Electromagnetic current correlations in reduced quantum electrodynamics, Phys. Rev. D 86 (2012) 025005 [arXiv:1204.5664] [INSPIRE].
S. Teber and A.V. Kotikov, Interaction corrections to the minimal conductivity of graphene via dimensional regularization, EPL 107 (2014) 57001 [arXiv:1407.7501] [INSPIRE].
A. Karch and Y. Sato, Conformal Manifolds with Boundaries or Defects, JHEP 07 (2018) 156 [arXiv:1805.10427] [INSPIRE].
D. Dudal, A.J. Mizher and P. Pais, Exact quantum scale invariance of three-dimensional reduced QED theories, Phys. Rev. D 99 (2019) 045017 [arXiv:1808.04709] [INSPIRE].
L. Di Pietro, D. Gaiotto, E. Lauria and J. Wu, 3d Abelian Gauge Theories at the Boundary, JHEP 05 (2019) 091 [arXiv:1902.09567] [INSPIRE].
C.P. Herzog and A. Shrestha, Two point functions in defect CFTs, JHEP 04 (2021) 226 [arXiv:2010.04995] [INSPIRE].
D.C. Pedrelli, D.T. Alves and V.S. Alves, Two-loop photon self-energy in pseudoquantum electrodynamics in the presence of a conducting surface, Phys. Rev. D 102 (2020) 125032 [INSPIRE].
M. Heydeman, C.B. Jepsen, Z. Ji and A. Yarom, Renormalization and conformal invariance of non-local quantum electrodynamics, JHEP 08 (2020) 007 [arXiv:2003.07895] [INSPIRE].
C.P. Herzog and A. Shrestha, Conformal surface defects in Maxwell theory are trivial, JHEP 08 (2022) 282 [arXiv:2202.09180] [INSPIRE].
G.W. Semenoff, Chiral Symmetry Breaking in Graphene, Phys. Scripta T 146 (2012) 014016 [arXiv:1108.2945] [INSPIRE].
M. Frasca, A. Ghoshal and N. Okada, Confinement and renormalization group equations in string-inspired nonlocal gauge theories, Phys. Rev. D 104 (2021) 096010 [arXiv:2106.07629] [INSPIRE].
P. Basteiro, J. Elfert, J. Erdmenger and H. Hinrichsen, Fractional Klein–Gordon equation on AdS2+1, J. Phys. A 55 (2022) 364002 [arXiv:2201.10870] [INSPIRE].
M.E. Fisher, S.-K. Ma and B.G. Nickel, Critical Exponents for Long-Range Interactions, Phys. Rev. Lett. 29 (1972) 917 [INSPIRE].
J. Sak, Recursion Relations and Fixed Points for Ferromagnets with Long-Range Interactions, Phys. Rev. B 8 (1973) 281.
J. Honkonen and M.Y. Nalimov, Crossover between field theories with short range and long range exchange or correlations, J. Phys. A 22 (1989) 751 [INSPIRE].
J. Honkonen, Critical behavior of the long range (ϕ2)2 model in the short range limit, J. Phys. A 23 (1990) 825 [INSPIRE].
T. Koffel, M. Lewenstein and L. Tagliacozzo, Entanglement entropy for the long range Ising chain, Phys. Rev. Lett. 109 (2012) 267203 [arXiv:1207.3957] [INSPIRE].
C. Behan, L. Rastelli, S. Rychkov and B. Zan, Long-range critical exponents near the short-range crossover, Phys. Rev. Lett. 118 (2017) 241601 [arXiv:1703.03430] [INSPIRE].
C. Behan, L. Rastelli, S. Rychkov and B. Zan, A scaling theory for the long-range to short-range crossover and an infrared duality, J. Phys. A 50 (2017) 354002 [arXiv:1703.05325] [INSPIRE].
D. Benedetti, R. Gurau, S. Harribey and K. Suzuki, Long-range multi-scalar models at three loops, J. Phys. A 53 (2020) 445008 [arXiv:2007.04603] [INSPIRE].
L. Caffarelli and L. Silvestre, An extension problem related to the fractional Laplacian, Commun. Part. Diff. Eq. 32 (2007) 1245 [math/0608640].
Y. Oz, Spontaneous Symmetry Breaking, Conformal Anomaly and Incompressible Fluid Turbulence, JHEP 11 (2017) 040 [arXiv:1707.07855] [INSPIRE].
T. Levy, Y. Oz and A. Raviv-Moshe, \( \mathcal{N} \) = 1 Liouville SCFT in Four Dimensions, JHEP 12 (2018) 122 [arXiv:1810.02746] [INSPIRE].
T. Levy, Y. Oz and A. Raviv-Moshe, \( \mathcal{N} \) = 2 Liouville SCFT in four dimensions, JHEP 10 (2019) 006 [arXiv:1907.08961] [INSPIRE].
A.C. Kislev, T. Levy and Y. Oz, Odd dimensional nonlocal Liouville conformal field theories, JHEP 07 (2022) 150 [arXiv:2206.10884] [INSPIRE].
N. Chai, A. Dymarsky and M. Smolkin, Model of Persistent Breaking of Discrete Symmetry, Phys. Rev. Lett. 128 (2022) 011601 [arXiv:2106.09723] [INSPIRE].
N. Chai et al., A model of persistent breaking of continuous symmetry, SciPost Phys. 12 (2022) 181 [arXiv:2111.02474] [INSPIRE].
G. La Nave, K. Limtragool and P.W. Phillips, Fractional Electromagnetism in Quantum Matter and High-Energy Physics, Rev. Mod. Phys. 91 (2019) 021003 [arXiv:1904.01023] [INSPIRE].
H. Kleinert, F.S. Nogueira and A. Sudbo, Kosterlitz-Thouless - like deconfinement mechanism in the (2+1)-dimensional Abelian Higgs model, Nucl. Phys. B 666 (2003) 361 [hep-th/0209132] [INSPIRE].
I.F. Herbut and B.H. Seradjeh, Permanent confinement in the compact QED(3) with fermionic matter, Phys. Rev. Lett. 91 (2003) 171601 [cond-mat/0305296] [INSPIRE].
R.L.P.G. do Amaral and E.C. Marino, Canonical quantization of theories containing fractional powers of the d’Alembertian operator, J. Phys. A 25 (1992) 5183 [INSPIRE].
E.C. Marino, L.O. Nascimento, V.S. Alves and C.M. Smith, Unitarity of theories containing fractional powers of the d’Alembertian operator, Phys. Rev. D 90 (2014) 105003 [arXiv:1408.1637] [INSPIRE].
B. Basa, G. La Nave and P.W. Phillips, Classification of nonlocal actions: Area versus volume entanglement entropy, Phys. Rev. D 101 (2020) 106006 [arXiv:1907.09494] [INSPIRE].
G. Calcagni, Quantum scalar field theories with fractional operators, Class. Quant. Grav. 38 (2021) 165006 [arXiv:2102.03363] [INSPIRE].
C. Heredia and J. Llosa, Nonlocal Lagrangian fields: Noether’s theorem and Hamiltonian formalism, Phys. Rev. D 105 (2022) 126002.
G. Calcagni and L. Rachwał, Ultraviolet-complete quantum field theories with fractional operators, arXiv:2210.04914 [INSPIRE].
G. Kleppe and R.P. Woodard, Nonlocal Yang-Mills, Nucl. Phys. B 388 (1992) 81 [hep-th/9203016] [INSPIRE].
W. Li and T. Takayanagi, Holography and Entanglement in Flat Spacetime, Phys. Rev. Lett. 106 (2011) 141301 [arXiv:1010.3700] [INSPIRE].
D. Gaiotto, A. Kapustin, N. Seiberg and B. Willett, Generalized Global Symmetries, JHEP 02 (2015) 172 [arXiv:1412.5148] [INSPIRE].
A.M. Polyakov, Compact Gauge Fields and the Infrared Catastrophe, Phys. Lett. B 59 (1975) 82 [INSPIRE].
S.S. Pufu, Anomalous dimensions of monopole operators in three-dimensional quantum electrodynamics, Phys. Rev. D 89 (2014) 065016 [arXiv:1303.6125] [INSPIRE].
E. Dyer, M. Mezei and S.S. Pufu, Monopole Taxonomy in Three-Dimensional Conformal Field Theories, arXiv:1309.1160 [INSPIRE].
S.M. Chester and S.S. Pufu, Towards bootstrapping QED3, JHEP 08 (2016) 019 [arXiv:1601.03476] [INSPIRE].
V.S. Alves, M. Gomes, A.Y. Petrov and A.J. da Silva, On the supersymmetric pseudo-QED, Phys. Lett. B 840 (2023) 137856 [arXiv:2209.07486] [INSPIRE].
A. Huang, B. Stoica, S.-T. Yau and X. Zhong, Green’s functions for Vladimirov derivatives and Tate’s thesis, Commun. Num. Theor. Phys. 15 (2021) 315 [arXiv:2001.01721] [INSPIRE].
S.S. Gubser et al., Non-local non-linear sigma models, JHEP 09 (2019) 005 [arXiv:1906.10281] [INSPIRE].
P.W. Phillips and G. La Nave, Nöther’s Second Theorem as an Obstruction to Charge Quantization, Springer Proc. Math. Stat. 335 (2019) 135 [arXiv:1911.05750] [INSPIRE].
E. Witten, Field Theory, Lecture 7, Quantum Field Theory program at IAS: Spring Term, notes by David Morrison (1997).
A. Kapustin and M.J. Strassler, On mirror symmetry in three-dimensional Abelian gauge theories, JHEP 04 (1999) 021 [hep-th/9902033] [INSPIRE].
O.I. Motrunich and A. Vishwanath, Emergent photons and new transitions in the O(3) sigma model with hedgehog suppression, Phys. Rev. B 70 (2004) 075104 [cond-mat/0311222] [INSPIRE].
J. Preskill, Magnetic monopoles, Ann. Rev. Nucl. Part. Sci. 34 (1984) 461 [INSPIRE].
A. Duncan, E. Eichten and H. Thacker, Electromagnetic splittings and light quark masses in lattice QCD, Phys. Rev. Lett. 76 (1996) 3894 [hep-lat/9602005] [INSPIRE].
RM123 collaboration, Leading isospin breaking effects on the lattice, Phys. Rev. D 87 (2013) 114505 [arXiv:1303.4896] [INSPIRE].
C. Bonati, A. Pelissetto and E. Vicari, Lattice Abelian-Higgs model with noncompact gauge fields, Phys. Rev. B 103 (2021) 085104 [arXiv:2010.06311] [INSPIRE].
T. Sulejmanpasic and C. Gattringer, Abelian gauge theories on the lattice: θ-Terms and compact gauge theory with(out) monopoles, Nucl. Phys. B 943 (2019) 114616 [arXiv:1901.02637] [INSPIRE].
P. Gorantla, H.T. Lam, N. Seiberg and S.-H. Shao, A modified Villain formulation of fractons and other exotic theories, J. Math. Phys. 62 (2021) 102301 [arXiv:2103.01257] [INSPIRE].
D.J. Amit, Y.Y. Goldschmidt and G. Grinstein, Renormalization Group Analysis of the Phase Transition in the 2D Coulomb Gas, Sine-Gordon Theory and xy Model, J. Phys. A 13 (1980) 585 [INSPIRE].
V. Arnold, Geometrical Methods In The Theory Of Ordinary Differential Equations, Springer-Verlag (1988).
A.M. Polyakov, Quark Confinement and Topology of Gauge Groups, Nucl. Phys. B 120 (1977) 429 [INSPIRE].
M. Karliner and G. Mack, Mass Gap and String Tension in QED Comparison of Theory With Monte Carlo Simulation, Nucl. Phys. B 225 (1983) 371 [INSPIRE].
M. Caselle, F. Gliozzi, U. Magnea and S. Vinti, Width of long color flux tubes in lattice gauge systems, Nucl. Phys. B 460 (1996) 397 [hep-lat/9510019] [INSPIRE].
M.J. Teper, SU(N) gauge theories in (2+1)-dimensions, Phys. Rev. D 59 (1999) 014512 [hep-lat/9804008] [INSPIRE].
M. Caselle, M. Hasenbusch and M. Panero, Comparing the Nambu-Goto string with LGT results, JHEP 03 (2005) 026 [hep-lat/0501027] [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].
A. Athenodorou and M. Teper, On the spectrum and string tension of U(1) lattice gauge theory in 2 + 1 dimensions, JHEP 01 (2019) 063 [arXiv:1811.06280] [INSPIRE].
Acknowledgments
The authors are grateful to Shai Chester, Mykola Dedushenko, Igor Klebanov, Petr Kravchuk, Silviu Pufu, Samson Shatashvili, and Edward Witten for helpful comments and illuminating discussions. M.H. is supported by the U.S. Department of Energy Grant DE-SC0009988 and the Institute for Advanced Study. Z.J. is supported by the ERC-COG grant NP-QFT No. 864583 “Non-perturbative dynamics of quantum fields: from new deconfined phases of matter to quantum black holes”, by the MIUR-SIR grant RBSI1471GJ, and by the INFN “Iniziativa Specifica ST&FI”. AY is supported in part by an Israeli Science Foundation excellence center grant 2289/18.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2212.11568
Rights and permissions
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.
About this article
Cite this article
Heydeman, M., Jepsen, C.B., Ji, Z. et al. Polyakov’s confinement mechanism for generalized Maxwell theory. J. High Energ. Phys. 2023, 119 (2023). https://doi.org/10.1007/JHEP04(2023)119
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2023)119