nLab superinsulator

Idea

In solid state physics, by super-insulators one refers to meaterials which at very low but non-vanishing temperature have effectively unbounded electrical resistance. This phenomenon may be understood as the “EM-dual” to that of superconductors.

Generalized to color charge, this notion plays a central role in the dual superconductor model of confinement.

References

General

See also:

• Wikipedia: Superinsulator

Dual superconductor model of confinement

General

Precursor discussion identifying the Polyakov dual flux tube strings as (akin to) vortices in a superconductor medium:

• Holger Bech Nielsen, Poul Olesen: Vortex-line models for dual strings, Nuclear Physics B 61 (1973) 45-61 [doi:10.1016/0550-3213(73)90350-7]

• Yoichiro Nambu: Strings, monopoles, and gauge fields, Phys. Rev. D 10 (1974) 4262 [doi:10.1103/PhysRevD.10.4262]

The articles now credited with (independently) proposing the dual superconductor model of color confinement:

• Stanley Mandelstam: Vortices and quark confinement in non-abelian gauge theories, Physics Letters B 53 5 (1975) 476–478 [doi:10.1016/0370-2693(75)90221-X]

• Gerard ’t Hooft; p 4-5 in: Gauge Fields with Unified Weak, Electromagnetic, and Strong Interactions, Rapporteur’s talk at E.P.S. International Conference on High Energy Physics, Palermo, Sicily (June 1975) [spire:2781, pdf, pdf]

• Gerard ’t Hooft: On the phase transition towards permanent quark confinement, Nuclear Physics B 138 1 (1978) 1–25 [doi:10.1016/0550-3213(78)90153-0]

Further discussion:

• Grigorios I. Poulis: Abelian dominance and adjoint sources in lattice QCD, Phys. Rev.D 54 (1996) 6974–6985 [doi:10.1103/PhysRevD.54.6974, arXiv:hep-lat/9601013]

• L. Del Debbio, M. Faber, Jeff Greensite, S. Olejnik: Some Cautionary Remarks on Abelian Projection and Abelian Dominance, Nucl. Phys. Proc. Suppl. 53 (1997) 141–147 [doi:10.1016/S0920-5632(96)00608-1, arXiv:hep-lat/9607053]

• Hiroko Ichie, Hideo Suganuma: Abelian dominance for confinement and random phase property of off-diagonal gluons in the maximally abelian gauge, Nuclear Physics B 548 1–-3 (1999) 365-382 [doi:10.1016/S0550-3213(99)00132-7, arXiv:hep-lat/9807025]

• John Ellis, N. E. Mavromatos: Confinement in Gauge Theories from the Condensation of World-Sheet Defects in Liouville String, Int . J. Mod. Phys. A 14 (1999) 3761–3788 [doi:10.1142/S0217751X99001743, arXiv:hep-th/9808172]

• Y. M. Cho, D. G. Pak: Magnetic Confinement in QCD, J. Korean Phys. Soc. 38 (2001) 151–154 [arXiv:hep-th/9906198]

• Y. M. Cho, D. G. Pak: Dynamical Symmetry Breaking and Magnetic Confinement in QCD [arXiv:hep-th/0006051]

• Y. M. Cho, D. G. Pak: Monopole condensation in $SU(2)$ QCD, Phys. Rev. D 65 (2002) 074027 [doi:10.1103/PhysRevD.65.074027, arXiv:hep-th/0201179]

• Kei-Ichi Kondo: Gauge-invariant gluon mass, infrared Abelian dominance and stability of magnetic vacuum, Phys. Rev. D 74 (2006) 125003 [doi:10.1103/PhysRevD.74.125003, arXiv:hep-th/0609166]

• Kei-Ichi Kondo, A. Shibata, T. Shinohara, S. Kato: Non-Abelian Dual Superconductor Picture for Quark Confinement, Phys. Rev. D 83 (2011) 114016 [doi:10.1103/PhysRevD.83.114016, arXiv:1007.2696]

• Y. M. Cho: Dimensional Transmutation by Monopole Condensation in QCD, Phys. Rev. D. 87 (2013) 085025 [doi:10.1103/PhysRevD.87.085025, arXiv:1206.6936]

• Y. M. Cho: Monopole Condensation and Mass Gap in $SU(3)$ QCD, International Journal of Modern Physics A 29 03n04 (2014) 1450013 [doi:10.1142/S0217751X14500134]

Review:

• Thomas Schaefer, Edward Shuryak; section III D of: Instantons in QCD, Rev. Mod. Phys. 70 (1998) 323–426 [doi:10.1103/RevModPhys.70.323, arXiv:hep-ph/9610451]

• Adriano Di Giacomo: Confinement of Color by Dual Superconductivity, Acta Physica Polonica B 28 12 (1997)

• Jeff Greensite: The Confinement Problem in Lattice Gauge Theory, Prog. Part. Nucl. Phys. 51 (2003) 1 [doi:10.1016/S0146-6410(03)90012-3, arXiv:hep-lat/0301023]

• Adriano Di Giacomo: Confinement of Color: Recent Progress [arXiv:hep-lat/0310021]

• Georges Ripka: Dual superconductor models of color confinement, Lecture Notes in Physics 639, Springer (2004) [doi:10.1007/b94800, arXiv:hep-ph/0310102]

• Adriano Di Giacomo: A Strategy to Study Confinement in QCD, Braz. J. Phys. 37 (2007) 208–213 [arXiv:hep-lat/0610027]

• Adriano Di Giacomo: Confinement by dual superconductivity: an update (2001) [pdf]

• Adriano Di Giacomo: The Dual Superconductor Picture for Confinement, in: Confinement, Duality, and Non-Perturbative Aspects of QCD, NATO Science Series: B 368, Springer (2002) 415–437 [doi:10.1007/0-306-47056-X_15]

• Kei-Ichi Kondo, Seikou Kato, Akihiro Shibata, Toru Shinohara: Quark confinement: Dual superconductor picture based on a non-Abelian Stokes theorem and reformulations of Yang–Mills theory, Physics Reports 579 (2015) 1–226 [doi:10.1016/j.physrep.2015.03.002]

  (emphasis on role of nonabelian Stokes theorem)

• Maxim Chernodub: QCD Vacuum as Dual Superconductor: Quark Confinement and Topology, Handbook of Nuclear Physics, Springer (2023) [doi:10.1007/978-981-19-6345-2_23]

See also:

• Tereza Mendes, Luis E. Oxman, Gustavo M. Simões, Rafael C. S. Tonhon: Cartan Fluxes in $SU(3)$ Lattice Gauge Theory [arXiv:2604.25003]

The DGC-decomposition

On decomposing, in a gauge invariant way, the gauge potential into an abelian background and nonabelian fluctuations:

The original articles:

• Yi-Shi Duan, Mo-Lin Ge: $SU(2)$ gauge theory and electrodynamics of $N$ moving magnetic monopoles, Scientia Sinica Mathematica 9 11 (1979) 1072–1081, reprinted in: Memorial Volume for Yi-Shi Duan, World Scientific (2018) 1-15 [doi:10.1142/9789813237278_0001]

• Y. M. Cho: Colored Monopoles, Phys. Rev. Lett. 44 (1980) 1115, Erratum Phys. Rev. Lett. 44 (1980) 1566 [doi:10.1103/PhysRevLett.44.1115]

• Faddeev & Niemi 1999

Further discussion:

• Sergei V. Shabanov: An effective action for monopoles and knot solitons in Yang-Mills theory, Phys. Lett. B 458 (1999) 322–330 [doi:10.1016/S0370-2693(99)00612-7, arXiv:hep-th/9903223]

• Bae, Cho & Kim 2002

• Michael L. Walker, Steven Duplij: Cho-Duan-Ge decomposition of QCD in the constraintless Clairaut-type formalism, Phys. Rev. D 91 064022 (2015) [doi:10.1103/PhysRevD.91.064022, arXiv:1411.6968]

• Kei-Ichi Kondo, T. Murakami, T. Shinohara: Yang-Mills theory constructed from Cho–Faddeev–Niemi decomposition, Prog. Theor. Phys. 115 (2006) 201–216 [doi:10.1143/PTP.115.201, arXiv:hep-th/0504107]

• Kei-Ichi Kondo, T. Murakami, T. Shinohara: BRST symmetry of $SU(2)$ Yang-Mills theory in Cho–Faddeev–Niemi decomposition, Eur. Phys. J.C 42 (2005) 475–481 [doi:10.1140/epjc/s2005-02344-4, arXiv:hep-th/0504198]

  (via BRST cohomology)

Review:

• KKSS 2015 §3

Relation to Faddeev-Skyrme model

Relation (for gauge group $SU(2)$, hence with coset space the 2-sphere $\S^2 \simeq SU(2)/SU(1)$) to the Fadeev-Skyrme model and Hopfion-like knot field configurations:

• Ludvig Faddeev, Antti J. Niemi: Partially Dual variables in $SU(2)$ Yang-Mills Theory, Phys. Rev. Lett. 82 (1999) 1624–1627 [doi:10.1103/PhysRevLett.82.1624, arXiv:hep-th/9807069]

• Shabanov 1999

• W. S. Bae, Y. M. Cho, Sang-Woo Kim: QCD versus Skyrme-Faddeev Theory, Phys. Rev. D 65 (2002) 025005 [doi:10.1103/PhysRevD.65.025005, arXiv:hep-th/0105163]

In lattice gauge theory

On the dual superconductor model of confinement in view of lattice QCD computations/simulations:

• Michael E. Peskin: Mandelstam ‘t Hooft Duality in Abelian Lattice Models, Annals Phys. 113 (1978) 122 [doi:10.1016/0003-4916(78)90252-X]

• Tsuneo Suzuki, Ichiro Yotsuyanagi: Possible evidence for Abelian dominance in quark confinement, Phys. Rev. D 42 (1990) 4257(R) [doi:10.1103/PhysRevD.42.4257]

• Paolo Cea, Leonardo Cosmai: Lattice investigation of dual superconductor mechanism of confinement, Nuclear Physics B - Proceedings Supplements 30 (1993) 572–575 [doi:10.1016/0920-5632(93)90276-C]

• Paolo Cea, Leonardo Cosmai: Dual Superconductor Mechanism of Confinement on the Lattice, Nuov Cim A 107 (1994) 541547 [doi:10.1007/BF02768788, arXiv:hep-lat/9210030]

• Paolo Cea, Leonardo Cosmai: The $SU(2)$ Confining Vacuum as a Dual Superconductor, Nucl. Phys. Proc. Suppl. 47 (1996) 318–321 [doi:10.1016/0920-5632(96)00065-5, arXiv:hep-lat/9509007]

• Hideo Suganuma, H. Ichie, K. Amemiya: Origin of Abelian Dominance in QCD in the Maximally Abelian Gauge, in: Quark Confinement and the Hadron Spectrum III, World Scientific (2000) 207–210 [doi:10.1142/9789812793713_0026]

• Hideo Suganuma, Naoyuki Sakumichi: Perfect Abelian dominance of confinement in quark-antiquark potential in $SU(3)$ lattice QCD [arXiv:1412.8489]

• Hideo Suganuma, Naoyuki Sakumichi: The three-quark potential and perfect Abelian dominance in $SU(3)$ lattice QCD, PoS LATTICE2015 (2016) 323 [arXiv:1511.05244 hep-lat]

• Paolo Cea, Leonardo Cosmai, Francesca Cuteri, Alessandro Papa: Flux tubes in the QCD vacuum, Phys. Rev. D 95 (2017) 114511 [doi:10.1103/PhysRevD.95.114511, arXiv:1702.06437 hep-lat]

• Hideo Suganuma, Naoyuki Sakumichi: Monopole Dominance of Confinement in $SU(3)$ Lattice QCD, PoS 336 267 (2018) [arXiv:1812.06827 hep-lat, pos:336/267, pdf]

• Zeinab Dehghan, Manfried Faber: What do we know about the confinement mechanism?, Phys. Part. Nuclei 56 (2025) 1148–1154 [doi:10.1134/S1063779625700236, arXiv:2412.10767 hep-lat]

In super-Yang-Mills theory

The dual superconductor model of confinement becomes analytically exact in $\mathcal{N}-2$ $D=4$ super Yang-Mills theory (cf. Seiberg-Witten theory) when broken to $\mathcal{N}=1$:

• Nathan Seiberg, Edward Witten: Monopole Condensation, And Confinement in $\mathcal{N}=2$ Supersymmetric Yang-Mills Theory, Nucl. Phys. B 426 (1994) 19–52 Erratum-ibid. B 430 (1994) 485-0486 [doi:10.1016/0550-3213(94)90124-4, arXiv:hep-th/9407087]

• Nathan Seiberg, Edward Witten: Monopoles, Duality and Chiral Symmetry Breaking in $\mathcal{N}=2$ Supersymmetric QCD, Nucl. Phys. B 431 (1994) 484–550 [doi:10.1016/0550-3213(94)90214-3, arXiv:hep-th/9408099]

Reviews with discussion of the impact on confinement in plain YM:

• Alexei Yung: What Do We Learn about Confinement from the Seiberg-Witten Theory, 3rd Moscow School of Physics and 28th ITEP Winter School of Physics [spire:527017,arXiv:hep-th/0005088]

• Michael Dine: On the Possibility of Demonstrating Confinement in Non-Supersymmetric Theories by Deforming Confining Supersymmetric Theories [arXiv:2211.17134]

In solid state physics

On experimentally accessible analogs of the dual superconductor model of confinement in solid state physics:

• M. Cristina Diamantini, Carlo A. Trugenberger, Valeri M. Vinokur: Confinement and Asymptotic Freedom with Cooper pairs, Nature Comm. Phys. 1 77 (2018) [doi:10.1038/s42005-018-0073-9, arXiv:1807.01984]

• M. Cristina Diamantini, Carlo A. Trugenberger: Superinsulators: a toy realization of QCD in condensed matter, Ch. 23 in Roman Jackiw – 80th Birthday Festschrift, World Scientific (2020) 275-286 [arXiv:2008.12541]

Review:

• Carlo A. Trugenberger: Superinsulators, Bose Metals and High-$T_c$ Superconductors: The Quantum Physics of Emergent Magnetic Monopoles, World Scientific (2022) [doi:10.1142/12688]

• Carlo A. Trugenberger: Superinsulation: Magnetic Monopoles and Electric Confinement in Condensed Matter, talk at CQTS (Feb 2025) [slides:pdf]

Via holographics QCD

Discussion of the dual superconductor model of color confinement via holographic QCD:

• Tsung-Sheng Huang, Wen-Yu Wen: Holographic Model of Dual Superconductor for Quark Confinement [arXiv:1607.08171]

• Antón F. Faedo, Carlos Hoyos, Javier G. Subils: Monopoles and confinement in three dimensions from holography, J. High Energ. Phys. 2023 218 (2023) [doi:10.1007/JHEP03(2023)218, arXiv:2212.04996]