Abstract
This work studies domain walls between chirally-separated vacua in supersymmetric Yang-Mills theory (SYM) on ℝ3 × 𝕊1 in the semiclassical limit. For all gauge groups we explicitly find the electric fluxes of all BPS domain walls and fully characterize the representation that they form under the global symmetry of SYM. We compute the characters of these representations formed by the semiclassical domain walls. We also compute these characters for the worldvolume TQFTs appearing in the literature for SU(N) and Sp(N) gauge groups. We find complete agreement between the two computations, providing thus a dynamical test of the proposed worldvolume TQFTs. We also propose a new worldvolume TQFT for E6 domain walls, subjecting it to the same tests. Finally, we study deconfinement of quarks on domain walls for all gauge groups. We show that for all gauge groups confining strings (stable in the abelianized regime) can end on domain walls, regardless of whether or not the group has a center.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
B.S. Acharya and C. Vafa, On domain walls of N = 1 supersymmetric Yang-Mills in four-dimensions, hep-th/0103011 [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, A note on domain walls and the parameter space of N = 1 gauge theories, JHEP 10 (2003) 021 [hep-th/0308144] [INSPIRE].
M.M. Anber, E. Poppitz and T. Sulejmanpašic, Strings from domain walls in supersymmetric Yang-Mills theory and adjoint QCD, Phys. Rev. D 92 (2015) 021701 [arXiv:1501.06773] [INSPIRE].
A.A. Cox, E. Poppitz and S.S.Y. Wong, Domain walls and deconfinement: a semiclassical picture of discrete anomaly inflow, JHEP 12 (2019) 011 [arXiv:1909.10979] [INSPIRE].
D. Delmastro and J. Gomis, Domain walls in \( 4d\mathcal{N} \) = 1 SYM, JHEP 03 (2021) 259 [arXiv:2004.11395] [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, Abelian duality, confinement, and chiral symmetry breaking in QCD(adj), Phys. Rev. Lett. 100 (2008) 032005 [arXiv:0708.1772] [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.W. Bub, E. Poppitz and S.S.Y. Wong, Confinement on ℝ3 × 𝕊1 and double-string collapse, JHEP 01 (2021) 044 [arXiv:2010.04330] [INSPIRE].
D. Gaiotto, A. Kapustin, N. Seiberg and B. Willett, Generalized Global Symmetries, JHEP 02 (2015) 172 [arXiv:1412.5148] [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].
S. Elitzur, G.W. Moore, A. Schwimmer and N. Seiberg, Remarks on the Canonical Quantization of the Chern-Simons-Witten Theory, Nucl. Phys. B 326 (1989) 108 [INSPIRE].
M. Shifman, Advanced Topics in Quantum Field Theory: A Lecture Course, second edition, Cambridge University Press (2022) [ISBN: 9781108840422].
M.M. Anber, E. Poppitz and B. Teeple, Deconfinement and continuity between thermal and (super) Yang-Mills theory for all gauge groups, JHEP 09 (2014) 040 [arXiv:1406.1199] [INSPIRE].
S. Cecotti and C. Vafa, On classification of N = 2 supersymmetric theories, Commun. Math. Phys. 158 (1993) 569 [hep-th/9211097] [INSPIRE].
E. Poppitz and M.E. Shalchian T., String tensions in deformed Yang-Mills theory, JHEP 01 (2018) 029 [arXiv:1708.08821] [INSPIRE].
J.E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge University Press (1990) [https://doi.org/10.1017/cbo9780511623646].
B.C. Hall, Lie Groups, Lie Algebras, and Representations, Springer, Cham (2015) [https://doi.org/10.1007/978-3-319-13467-3] [INSPIRE].
N. Iwahori and H. Matsumoto, On some bruhat decomposition and the structure of the hecke rings of p-Adic chevalley groups, Publ. Math. IHES 25 (1965) 5.
P.C. Argyres and M. Ünsal, The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects, JHEP 08 (2012) 063 [arXiv:1206.1890] [INSPIRE].
Acknowledgments
I am grateful to Erich Poppitz for his help and guidance throughout this project and for comments on this manuscript. I acknowledge the support of the Natural Sciences and Engineering Research Council of Canada (NSERC), funding reference number 559071 / 2021.
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: 2405.06053
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
Cox, A.A. Domain walls in super Yang-Mills: worldvolume TQFTs and deconfinement from semiclassics on ℝ3 × 𝕊1. J. High Energ. Phys. 2024, 58 (2024). https://doi.org/10.1007/JHEP08(2024)058
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2024)058