Orientifold and Integrability: 𝒩=4 Super-Yang-Mills on ℝℙ^4

Abstract

We study planar 𝒩=4 super Yang-Mills theory (SYM) on the real projective space ℝℙ⁴ using integrability, holography and supersymmetric localization, and discuss its relation to orientifolds in string theory. We show that the integrability of 𝒩=4 SYM is preserved when combining the ℤ₂ involution defining ℝℙ⁴ with the action of the charge conjugation of the SU(N) gauge group. We demonstrate this by calculating one-point functions of non-BPS single-trace operators in various subsectors at weak coupling, which can be mapped to overlaps between energy eigenstates and crosscap states in integrable spin chains. The results exhibit a parity selection rule, a hallmark of integrability, and are given in terms of a ratio of determinants. Building on these results, we conjecture a closed formula for general single-trace operators. We further provide evidence that this construction is holographically dual to a probe orientifold O1-plane in AdS₅× S⁵ by constructing the corresponding worldsheet crosscap states in the pp-wave limit. Finally, we use supersymmetric localization to compute one-point functions of half-BPS operators exactly at finite g_YM and N. The computation reduces to two-dimensional Yang-Mills theory on ℝℙ² twisted by charge conjugation and leads to a matrix integral of a Wishart-Laguerre type. In the planar limit, the exact result interpolates between the weak-coupling gauge-theory result, the strong-coupling supergravity prediction for the orientifold, and the worldsheet crosscap in the pp-wave limit.

Generalised Ω-backgrounds in twisted N=4 super Yang-Mills
Elisa Iris Marieni, Itamar Yaakov
arXiv29 Oct 2026PreprintCC BY 4.0Full textHigh-energy & particle physicsarXiv
The simplest event shape in 𝒩=4 super Yang--Mills
Carlos Bercini, Sidhaarth Kumar
arXiv13 Oct 2026PreprintCC BY 4.0Full textHigh-energy & particle physicsarXiv
Energy-energy correlators in the large-charge limit of 𝒩=4 super Yang-Mills theory
Alessandro Georgoudis, Max Jackson, Congkao Wen
arXiv8 Oct 2026PreprintarXiv licenceFull textHigh-energy & particle physicsarXiv
𝒩=4 Super Yang-Mills Flux Tube in AdS
Victor Gorbenko, Orr Sela, Brian R. Zielazienski
arXiv29 Oct 2026PreprintCC BY 4.0Full textHigh-energy & particle physicsarXiv
Surface defects in 𝒩=4 Super Yang-Mills: exact results and holographic bootstrap
Lorenzo Bianchi, Davide Bonomi, Maddalena Ferragatta +1
HAL19 Oct 2026PreprintarXiv licenceFull textHigh-energy & particle physicsHALarXiv

Cite

BibTeX RIS

BibTeX

@misc{caetano2026orientifold,
  title = {{Orientifold and Integrability: $\mathcalN=4$ Super-Yang-Mills on $\mathbbRP^4$}},
  author = {Joao Caetano and Shota Komatsu and Paolo Soresina and Anders Wallberg},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.28725},
  eprint = {2610.28725},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.28725},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Orientifold and Integrability: 𝒩=4 Super-Yang-Mills on ℝℙ^4
AU  - Joao Caetano
AU  - Shota Komatsu
AU  - Paolo Soresina
AU  - Anders Wallberg
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.28725
UR  - https://arxiv.org/abs/2610.28725
AB  - We study planar 𝒩=4 super Yang-Mills theory (SYM) on the real projective space ℝℙ^4 using integrability, holography and supersymmetric localization, and discuss its relation to orientifolds in string theory. We show that the integrability of 𝒩=4 SYM is preserved when combining the ℤ_2 involution defining ℝℙ^4 with the action of the charge conjugation of the SU(N) gauge group. We demonstrate this by calculating one-point functions of non-BPS single-trace operators in various subsectors at weak coupling, which can be mapped to overlaps between energy eigenstates and crosscap states in integrable spin chains. The results exhibit a parity selection rule, a hallmark of integrability, and are given in terms of a ratio of determinants. Building on these results, we conjecture a closed formula for general single-trace operators. We further provide evidence that this construction is holographically dual to a probe orientifold O1-plane in AdS_5× S^5 by constructing the corresponding worldsheet crosscap states in the pp-wave limit. Finally, we use supersymmetric localization to compute one-point functions of half-BPS operators exactly at finite g_YM and N. The computation reduces to two-dimensional Yang-Mills theory on ℝℙ^2 twisted by charge conjugation and leads to a matrix integral of a Wishart-Laguerre type. In the planar limit, the exact result interpolates between the weak-coupling gauge-theory result, the strong-coupling supergravity prediction for the orientifold, and the worldsheet crosscap in the pp-wave limit.
ER  -

Orientifold and Integrability: 𝒩=4 Super-Yang-Mills on ℝℙ⁴

Abstract

Related

Cite