Abstract
We study the physics of quark deconfinement on domain walls in four-di- mensional supersymmetric SU(N) Yang-Mills theory, compactified on a small circle with supersymmetric boundary conditions. We numerically examine the properties of BPS domain walls connecting vacua k units apart. We also determine their electric fluxes and use the results to show that Wilson loops of any nonzero N -ality exhibit perimeter law on all k-walls. Our results confirm and extend, to all N and k, the validity of the semiclassical picture of deconfinement of Anber, Sulejmanpasic and one of us (EP), arXiv:1501.06773, providing a microscopic explanation of mixed 0-form/1-form anomaly inflow.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
N. Seiberg and E. Witten, Gauge dynamics and compactification to three-dimensions, in proceedings of the Conference on the Mathematical Beauty of Physics (In Memory of C. Itzykson), Saclay, France, 5–7 June 1996, pp. 333–366 [hep-th/9607163] [INSPIRE].
O. Aharony, A. Hanany, K.A. Intriligator, N. Seiberg and M.J. Strassler, Aspects of N = 2 supersymmetric gauge theories in three-dimensions, Nucl. Phys.B 499 (1997) 67 [hep-th/9703110] [INSPIRE].
N.M. Davies, T.J. Hollowood, V.V. Khoze and M.P. Mattis, Gluino condensate and magnetic monopoles in supersymmetric gluodynamics, Nucl. Phys.B 559 (1999) 123 [hep-th/9905015] [INSPIRE].
N.M. Davies, T.J. Hollowood and V.V. Khoze, Monopoles, affine algebras and the gluino condensate, J. Math. Phys.44 (2003) 3640 [hep-th/0006011] [INSPIRE].
M. Ünsal, Magnetic bion condensation: A New mechanism of confinement and mass gap in four dimensions, Phys. Rev.D 80 (2009) 065001 [arXiv:0709.3269] [INSPIRE].
M. Ünsal, Abelian Duality, Confinement, and Chiral-Symmetry Breaking in a SU(2) QCD-Like Theory, Phys. Rev. Lett.100 (2008) 032005 [arXiv:0708.1772] [INSPIRE].
E. Poppitz and M. Ünsal, Seiberg-Witten and ‘Polyakov-like’ magnetic bion confinements are continuously connected, JHEP07 (2011) 082 [arXiv:1105.3969] [INSPIRE].
E. Poppitz, T. Schäfer and M. Ünsal, Continuity, Deconfinement and (Super) Yang-Mills Theory, JHEP10 (2012) 115 [arXiv:1205.0290] [INSPIRE].
P.C. Argyres and M. Ünsal, The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion and renormalon effects, JHEP08 (2012) 063 [arXiv:1206.1890] [INSPIRE].
P. Argyres and M. Ünsal, A semiclassical realization of infrared renormalons, Phys. Rev. Lett.109 (2012) 121601 [arXiv:1204.1661] [INSPIRE].
E. Poppitz, T. Schäfer and M. Ünsal, Universal mechanism of (semi-classical) deconfinement and theta-dependence for all simple groups, JHEP03 (2013) 087 [arXiv:1212.1238] [INSPIRE].
K.-M. Lee and P. Yi, Monopoles and instantons on partially compactified D-branes, Phys. Rev.D 56 (1997) 3711 [hep-th/9702107] [INSPIRE].
T.C. Kraan and P. van Baal, Periodic instantons with nontrivial holonomy, Nucl. Phys.B 533 (1998) 627 [hep-th/9805168] [INSPIRE].
A.M. Polyakov, Quark Confinement and Topology of Gauge Groups, Nucl. Phys.B 120 (1977) 429 [INSPIRE].
G. Bergner, P. Giudice, G. Münster and S. Piemonte, Witten index and phase diagram of compactified \( \mathcal{N} \) = 1 supersymmetric Yang-Mills theory on the lattice, PoS(LATTICE2015)239 (2016) [arXiv:1510.05926] [INSPIRE].
G. Bergner, S. Piemonte and M. Ünsal, Adiabatic continuity and confinement in supersymmetric Yang-Mills theory on the lattice, JHEP11 (2018) 092 [arXiv:1806.10894] [INSPIRE].
G. Bergner, C. López and S. Piemonte, Study of center and chiral symmetry realization in thermal \( \mathcal{N} \) = 1 super Yang-Mills theory using the gradient flow, Phys. Rev.D 100 (2019) 074501 [arXiv:1902.08469] [INSPIRE].
G.V. Dunne and M. Ünsal, New Nonperturbative Methods in Quantum Field Theory: From Large-N Orbifold Equivalence to Bions and Resurgence, Ann. Rev. Nucl. Part. Sci.66 (2016) 245 [arXiv:1601.03414] [INSPIRE].
M.M. Anber, E. Poppitz and T. Sulejmanpasic, Strings from domain walls in supersymmetric Yang-Mills theory and adjoint QCD, Phys. Rev.D 92 (2015) 021701 [arXiv:1501.06773] [INSPIRE].
S.-J. Rey, unpublished (1997).
E. Witten, Branes and the dynamics of QCD, Nucl. Phys.B 507 (1997) 658 [hep-th/9706109] [INSPIRE].
A. Armoni and M. Shifman, On k string tensions and domain walls in N = 1 gluodynamics, Nucl. Phys.B 664 (2003) 233 [hep-th/0304127] [INSPIRE].
M. Ünsal and L.G. Yaffe, Center-stabilized Yang-Mills theory: Confinement and large N volume independence, Phys. Rev.D 78 (2008) 065035 [arXiv:0803.0344] [INSPIRE].
D. Gaiotto, A. Kapustin, N. Seiberg and B. Willett, Generalized Global Symmetries, JHEP02 (2015) 172 [arXiv:1412.5148] [INSPIRE].
D. Gaiotto, A. Kapustin, Z. Komargodski and N. Seiberg, Theta, Time Reversal and Temperature, JHEP05 (2017) 091 [arXiv:1703.00501] [INSPIRE].
D. Gaiotto, Z. Komargodski and N. Seiberg, Time-reversal breaking in QCD4 , walls and dualities in 2 + 1 dimensions, JHEP01 (2018) 110 [arXiv:1708.06806] [INSPIRE].
T. Sulejmanpasic, H. Shao, A. Sandvik and M. Ünsal, Confinement in the bulk, deconfinement on the wall: infrared equivalence between compactified QCD and quantum magnets, Phys. Rev. Lett.119 (2017) 091601 [arXiv:1608.09011] [INSPIRE].
Z. Komargodski, T. Sulejmanpasic and M. Ünsal, Walls, anomalies and deconfinement in quantum antiferromagnets, Phys. Rev.B 97 (2018) 054418 [arXiv:1706.05731] [INSPIRE].
P. Draper, Domain Walls and the C P Anomaly in Softly Broken Supersymmetric QCD, Phys. Rev.D 97 (2018) 085003 [arXiv:1801.05477] [INSPIRE].
A. Ritz and A. Shukla, Domain wall moduli in softly-broken SQCD at \( \overline{\theta} \) = π, Phys. Rev.D 97 (2018) 105015 [arXiv:1804.01978] [INSPIRE].
M.M. Anber and E. Poppitz, Domain walls in high-T SU(N ) super Yang-Mills theory and QCD(adj), JHEP05 (2019) 151 [arXiv:1811.10642] [INSPIRE].
M.M. Anber and E. Poppitz, Anomaly matching, (axial) Schwinger models and high-T super Yang-Mills domain walls, JHEP09 (2018) 076 [arXiv:1807.00093] [INSPIRE].
H. Nishimura and Y. Tanizaki, High-temperature domain walls of QCD with imaginary chemical potentials, JHEP06 (2019) 040 [arXiv:1903.04014] [INSPIRE].
T. Misumi, Y. Tanizaki and M. Ünsal, Fractional θ angle, ’t Hooft anomaly and quantum instantons in charge-q multi-flavor Schwinger model, JHEP07 (2019) 018 [arXiv:1905.05781] [INSPIRE].
C. Córdova, D.S. Freed, H.T. Lam and N. Seiberg, Anomalies in the Space of Coupling Constants and Their Dynamical Applications I, arXiv:1905.09315 [INSPIRE].
C. Córdova, D.S. Freed, H.T. Lam and N. Seiberg, Anomalies in the Space of Coupling Constants and Their Dynamical Applications II, arXiv:1905.13361 [INSPIRE].
B.S. Acharya and C. Vafa, On domain walls of N = 1 supersymmetric Yang-Mills in four-dimensions, hep-th/0103011 [INSPIRE].
D. Gaiotto, Kazama-Suzuki models and BPS domain wall junctions in N = 1 SU(N ) Super Yang-Mills, arXiv:1306.5661 [INSPIRE].
M. Dierigl and A. Pritzel, Topological Model for Domain Walls in (Super-)Yang-Mills Theories, Phys. Rev.D 90 (2014) 105008 [arXiv:1405.4291] [INSPIRE].
K. Hori, A. Iqbal and C. Vafa, D-branes and mirror symmetry, hep-th/0005247 [INSPIRE].
A. Ritz, M. Shifman and A. Vainshtein, Counting domain walls in N = 1 superYang-Mills, Phys. Rev.D 66 (2002) 065015 [hep-th/0205083] [INSPIRE].
A. Ritz, M. Shifman and A. Vainshtein, Enhanced worldvolume supersymmetry and intersecting domain walls in N = 1 SQCD, Phys. Rev.D 70 (2004) 095003 [hep-th/0405175] [INSPIRE].
A. Ritz, Domain wall junctions in N = 1 super Yang-Mills and quantum Hall edges, in proceedings of the 7th Workshop on Continuous Advances in QCD , Minneapolis, Minnesota, U.S.A., 11–14 May 2006, World Scientific (2006), pp. 273–279.
R. Argurio, M. Bertolini, F. Bigazzi, A.L. Cotrone and P. Niro, QCD domain walls, Chern-Simons theories and holography, JHEP09 (2018) 090 [arXiv:1806.08292] [INSPIRE].
V. Bashmakov, F. Benini, S. Benvenuti and M. Bertolini, Living on the walls of super-QCD, SciPost Phys.6 (2019) 044 [arXiv:1812.04645] [INSPIRE].
P.-S. Hsin, H.T. Lam and N. Seiberg, Comments on One-Form Global Symmetries and Their Gauging in 3d and 4d, SciPost Phys.6 (2019) 039 [arXiv:1812.04716] [INSPIRE].
G.S. Bali, Baryons from the lattice: Past, present and future, in proceedings of the 3rd International Workshop on the Physics of Excited Nucleons (NSTAR 2002), Pittsburgh, Pennsylvania, U.S.A., 9–12 October 2002, pp. 61–72 [nucl-th/0302039] [INSPIRE].
N. Seiberg and E. Witten, Electric-magnetic duality, monopole condensation and confinement in N = 2 supersymmetric Yang-Mills theory, Nucl. Phys.B 426 (1994) 19 [Erratum ibid.B 430 (1994) 485] [hep-th/9407087] [INSPIRE].
M.R. Douglas and S.H. Shenker, Dynamics of SU(N) supersymmetric gauge theory, Nucl. Phys.B 447 (1995) 271 [hep-th/9503163] [INSPIRE].
E. Poppitz and M.E. Shalchian T., String tensions in deformed Yang-Mills theory, JHEP01 (2018) 029 [arXiv:1708.08821] [INSPIRE].
J. Greensite, An introduction to the confinement problem, Lect. Notes Phys.821 (2011) 1 [INSPIRE].
G.S. Bali, Casimir scaling of SU(3) static potentials, Phys. Rev.D 62 (2000) 114503 [hep-lat/0006022] [INSPIRE].
B. Bringoltz and M. Teper, Closed k-strings in SU(N ) gauge theories: 2 + 1 dimensions, Phys. Lett.B 663 (2008) 429 [arXiv:0802.1490] [INSPIRE].
A. Armoni, D. Dorigoni and G. Veneziano, k-String Tension from Eguchi-Kawai Reduction, JHEP10 (2011) 086 [arXiv:1108.6196] [INSPIRE].
J. Greensite, B. Lucini and A. Patella, k-string tensions and the 1/N expansion, Phys. Rev.D 83 (2011) 125019 [arXiv:1101.5344] [INSPIRE].
B. Lucini and M. Panero, SU(N ) gauge theories at large N , Phys. Rept.526 (2013) 93 [arXiv:1210.4997] [INSPIRE].
M.M. Anber and V. Pellizzani, Representation dependence of k-strings in pure Yang-Mills theory via supersymmetry, Phys. Rev.D 96 (2017) 114015 [arXiv:1710.06509] [INSPIRE].
G. Bergner, P. Giudice, G. Münster, I. Montvay and S. Piemonte, The light bound states of supersymmetric SU(2) Yang-Mills theory, JHEP03 (2016) 080 [arXiv:1512.07014] [INSPIRE].
S. Ali et al., The light bound states of \( \mathcal{N} \) = 1 supersymmetric SU(3) Yang-Mills theory on the lattice, JHEP03 (2018) 113 [arXiv:1801.08062] [INSPIRE].
S. Ali et al., Numerical results for the lightest bound states in \( \mathcal{N} \) = 1 supersymmetric SU(3) Yang-Mills theory, Phys. Rev. Lett.122 (2019) 221601 [arXiv:1902.11127] [INSPIRE].
M.M. Anber, E. Poppitz and B. Teeple, Deconfinement and continuity between thermal and (super) Yang-Mills theory for all gauge groups, JHEP09 (2014) 040 [arXiv:1406.1199] [INSPIRE].
M.M. Anber and T. Sulejmanpasic, The renormalon diagram in gauge theories on ℝ3× 𝕊1, JHEP01 (2015) 139 [arXiv:1410.0121] [INSPIRE].
A. Cherman and E. Poppitz, Emergent dimensions and branes from large-N confinement, Phys. Rev.D 94 (2016) 125008 [arXiv:1606.01902] [INSPIRE].
M.M. Anber and E. Poppitz, New nonperturbative scales and glueballs in confining supersymmetric gauge theories, JHEP03 (2018) 052 [arXiv:1711.00027] [INSPIRE].
K. Aitken, A. Cherman, E. Poppitz and L.G. Yaffe, QCD on a small circle, Phys. Rev.D 96 (2017) 096022 [arXiv:1707.08971] [INSPIRE].
M.M. Anber and E. Poppitz, On the global structure of deformed Yang-Mills theory and QCD(adj) on ℝ3× 𝕊1 , JHEP10 (2015) 051 [arXiv:1508.00910] [INSPIRE].
S. Chapra and R. Canale, Numerical Methods for Engineers, McGraw-Hill (2015).
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: 1909.10979
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
Cox, A.A., Poppitz, E. & Wong, S.S. Domain walls and deconfinement: a semiclassical picture of discrete anomaly inflow. J. High Energ. Phys. 2019, 11 (2019). https://doi.org/10.1007/JHEP12(2019)011
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2019)011