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<p>We investigate the symmetry structure of five-dimensional Yang-Mills theories with 𝔰𝔲(<i>N</i>) gauge algebra. These theories feature intertwined 0-, 1-, and 2-form symmetries, depending on the global variant one is considering. In the SU(<i>N</i>) theory, there is a mixed ’t Hooft anomaly between the instantonic 0-form symmetry and the electric 1-form symmetry. We show that in the PSU(<i>N</i>) theory this translates into a ℤ<sub><i>N</i></sub> extension of the instantonic symmetry, generated by an invertible condensation defect of the magnetic 2-form symmetry. We identify the charged configurations as linked ’t Hooft surfaces, while pointlike instanton operators remain insensitive to the extension. We generalize our analysis to the SU(<i>N</i>)/ℤ<sub><i>k</i></sub> global form and show that similar results hold, embedded now in a 3-group structure for generic <i>k</i>. We then apply our findings to SO(3) supersymmetric Yang-Mills theory. We determine the global form of the enhanced instantonic symmetry of its superconformal UV completion, showing that it arises through a similar symmetry extension mechanism from the parent <i>E</i><sub>1</sub> theory, which is the UV completion of SU(2) supersymmetric Yang-Mills theory. Finally, we recast our results in the language of the symmetry topological field theory. As a warm-up, we also analyze Maxwell theory, highlighting analogous features involving continuous symmetries and composite currents.</p>

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Symmetry extension by condensation defects in five-dimensional gauge theories

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月25日

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  • Matteo Bertolini,
  • Lorenzo Di Pietro,
  • Stefano C. Lanza,
  • Pierluigi Niro,
  • Antonio Santaniello

摘要

We investigate the symmetry structure of five-dimensional Yang-Mills theories with 𝔰𝔲(N) gauge algebra. These theories feature intertwined 0-, 1-, and 2-form symmetries, depending on the global variant one is considering. In the SU(N) theory, there is a mixed ’t Hooft anomaly between the instantonic 0-form symmetry and the electric 1-form symmetry. We show that in the PSU(N) theory this translates into a ℤN extension of the instantonic symmetry, generated by an invertible condensation defect of the magnetic 2-form symmetry. We identify the charged configurations as linked ’t Hooft surfaces, while pointlike instanton operators remain insensitive to the extension. We generalize our analysis to the SU(N)/ℤk global form and show that similar results hold, embedded now in a 3-group structure for generic k. We then apply our findings to SO(3) supersymmetric Yang-Mills theory. We determine the global form of the enhanced instantonic symmetry of its superconformal UV completion, showing that it arises through a similar symmetry extension mechanism from the parent E1 theory, which is the UV completion of SU(2) supersymmetric Yang-Mills theory. Finally, we recast our results in the language of the symmetry topological field theory. As a warm-up, we also analyze Maxwell theory, highlighting analogous features involving continuous symmetries and composite currents.