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arXiv · 2503.22598

Integrable Corners in the Space of Gukov-Witten Surface Defects

Adam Chalabi·Charlotte Kristjansen·Chenliang Su
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Abstract

We investigate integrability properties of Gukov-Witten 1/2-BPS surface defects in $SU(N)$ $\mathcal{N}=4$ super-Yang-Mills (SYM) theory in the large-$N$ limit. We demonstrate that ordinary Gukov-Witten defects, which depend on a set of continuous parameters, are not integrable except for special sub-sectors. In contrast to these, we show that rigid Gukov-Witten defects, which depend on a discrete parameter but not on continuous ones, appear integrable in a corner of the discrete parameter space. Whenever we find an integrable sector, we derive a closed-form factorised expression for the leading-order one-point function of unprotected operators built out of the adjoint scalars of $\mathcal{N}=4$ SYM theory. Our results raise the possibility of finding an all-loop formula for one-point functions of unprotected operators in the presence of a rigid Gukov-Witten defect at the corner in parameter space.

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Adam Chalabi, Charlotte Kristjansen, Chenliang Su. 2025-03-28. Integrable Corners in the Space of Gukov-Witten Surface Defects. https://arxiv.org/abs/2503.22598

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