An index for ray operators in 5d E_n SCFTs

Chi-Ming Chang Department of Physics, University of California, Berkeley, CA 94720, U.S.A. Ori J. Ganor Department of Physics, University of California, Berkeley, CA 94720, U.S.A. Jihwan Oh Department of Physics, University of California, Berkeley, CA 94720, U.S.A.

arXiv subject: High Energy Physics - Theory (hep-th) mathscidoc:2207.74009

Journal of High Energy Physics, 2017, (18), 2017.2
We construct an index for BPS operators supported on a ray in five dimensional superconformal field theories with exceptional global symmetries. We compute the E_n representations (for n = 2, . . . , 7) of operators of low spin, thus verifying that while the expression for the index is only SO(2n − 2) × U(1) invariant, the index itself exhibits the full E_n symmetry (at least up to the order we expanded). The ray operators we studied in 5d can be viewed as generalizations of operators constructed in a Yang-Mills theory with fundamental matter by attaching an open Wilson line to a quark. For n ≤ 7, in contrast to local operators, they carry nontrivial charge under the ℤ_{9 − n}  ⊂ E_n center of the global symmetry. The representations that appear in the ray operator index are therefore different, for n ≤ 7, from those appearing in the previously computed superconformal index. For 3 ≤ n ≤ 7, we find that the leading term in the index is a character of a minuscule representation of E_n . We also discuss the case n = 8, which presents a unique technical challenge, and remains an open problem.
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@inproceedings{chi-ming2017an,
  title={An index for ray operators in 5d E_n SCFTs},
  author={Chi-Ming Chang, Ori J. Ganor, and Jihwan Oh},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220702140135892580505},
  booktitle={Journal of High Energy Physics},
  volume={2017},
  number={18},
  year={2017},
}
Chi-Ming Chang, Ori J. Ganor, and Jihwan Oh. An index for ray operators in 5d E_n SCFTs. 2017. Vol. 2017. In Journal of High Energy Physics. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220702140135892580505.
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