Casimir operators of 4D , 𝒩=2 supersymmetry in the harmonic approach

@misc{eremeev2026casimir,
  title = {{Casimir operators of $4D\,, \mathcalN=2$ supersymmetry in the harmonic approach}},
  author = {Egor Eremeev and Evgeny Ivanov},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.27412},
  eprint = {2608.27412},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.27412},
}

TY  - UNPB
TI  - Casimir operators of 4D , 𝒩=2 supersymmetry in the harmonic approach
AU  - Egor Eremeev
AU  - Evgeny Ivanov
PY  - 2026
DA  - 2026/09/10
PB  - arXiv
DO  - 10.48550/arxiv.2608.27412
UR  - https://arxiv.org/abs/2608.27412
AB  - We construct Casimir operators of 4D, 𝒩=2 supersymmetry algebra in the harmonic superspace approach, and provide the explicit expressions for them in terms of covariant derivatives in the analytic basis. Specifically, the superisospin operator C_I is expressed in terms of new 'long' harmonic derivatives ∇^±±, ∇^0 as C_I = 1/4(∇^0)^2 + 1/2{∇^++,∇^−−}. These derivatives involve non-local terms with the inverse Box operator Box^−1 and satisfy modified SU(2) algebra relations in which the eigenvalues of ∇^0 on analytic superfields are shifted by -2 relative to the standard U(1) harmonic charges. We also construct 𝒩=2 superhelicity and super-isohelicity operators relevant to the massless case (with vanishing Box) and find their eigenvalues for few instructive examples of 4D, 𝒩=2 superfield theories.
ER  -