Circling in on correlation functions in 𝒩=2 orbifold theories

@misc{plat2026circling,
  title = {{Circling in on correlation functions in $\mathcalN=2$ orbifold theories}},
  author = {Dennis le Plat and Torben Skrzypek},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.28733},
  eprint = {2610.28733},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.28733},
}

TY  - UNPB
TI  - Circling in on correlation functions in 𝒩=2 orbifold theories
AU  - Dennis le Plat
AU  - Torben Skrzypek
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2610.28733
UR  - https://arxiv.org/abs/2610.28733
AB  - We review the harmonic superspace formalism for 4d 𝒩=2 theories and apply it to orbifolds of 𝒩=4 Super-Yang-Mills (SYM) theory. These theories have a remarkably similar description to 𝒩=4 SYM, but their planar supergraphs feature topological twist lines which generate phases when intersecting bifundamental hypermultiplet propagators. These cause twisted sector BPS correlators to depend on the coupling g. Twisted Coulomb-branch operators of length L receive a leading perturbative contribution to their two-point function at order 𝒪(g^2L) from a supergraph involving a wrapped hypermultiplet circle. After performing the complete D-algebra, we show that the supergraph reduces to the universal conformal period W_L=binom2LLζ(2L−1). We extend this analysis to multiple nested hypermultiplet circles and show that they reproduce a series of higher-order terms in the exact localisation result. A subsequent evaluation of leading contributions to BPS three-point correlators again shows complete agreement with localisation results in extremal case and generates new perturbative data in the non-extremal case. The latter involves one untwisted BPS descendant, which contains physical hypermultiplet fields and can therefore connect directly to the twist-dependent hypermultiplet circle. This reduces the suppression in g, resulting in a contribution 4 g^2(ℓ+1) W_ℓ+1 controlled by a bridge length ℓ rather than by an external operator length L≥ℓ. These examples demonstrate the feasibility of harmonic superspace calculations in orbifold theories and point to various future applications in the context of non-BPS correlators, integrability and marginal deformations.
ER  -