Surface defects in š¯’©=4 Super Yang-Mills: exact results and holographic bootstrap
Abstract
We study two-point functions of chiral primary operators in š¯’©=4 Super Yang-Mills in the presence of a half-BPS surface defect. Such a defect preserves only the diagonal combination of transverse rotations and of a global U(1) R-symmetry, so that the correlator depends on one additional cross-ratio and splits into sectors of definite angular charge. We solve the superconformal Ward identities and construct the bulk and defect superconformal blocks in all sectors, including the charged ones, which have no analogue for defects preserving transverse rotations. The solution contains a holomorphic sector, which we fix non-perturbatively by mapping it to a chiral algebra correlator. We extend this map to defects breaking transverse rotations, where it requires a redefinition of the modes of the two-dimensional current algebra, and use it to fix the charged sectors as well. We then use the defect dispersion relation to reconstruct the full correlator of the dimension-two chiral primary at leading order at large N and strong coupling. In the charged sectors long multiplets are absent and the answer is conjecturally exact in both N and the coupling; expanding it at weak coupling, we find perfect agreement with known results. From these correlators we extract infinitely many new pieces of defect CFT data. Finally, we reproduce the strong-coupling answer by an independent Witten diagram bootstrap on the rotation-invariant locus.
Related
- Pre-Strings Lectures on Holographic Correlators and Analytic Bootstrap
- Cusped Defects: Cusp Operator Expansion, Conformal Properties and Bootstrap Applications
- Super Liouville theory on the torus: bootstrap and the super Virasoro minimal string
- Symmetry breaking from conformality loss on holographic RĆ©nyi defects
- Aspects of Witten diagrams for holographic defects
BibTeX
@misc{bianchi2026surface,
title = {{Surface defects in $\mathcalN=4$ Super Yang-Mills: exact results and holographic bootstrap}},
author = {Lorenzo Bianchi and Davide Bonomi and Maddalena Ferragatta and Valentina Forini},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10723},
eprint = {2610.10723},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05835178v1},
}
RIS
TY - UNPB
TI - Surface defects in š¯’©=4 Super Yang-Mills: exact results and holographic bootstrap
AU - Lorenzo Bianchi
AU - Davide Bonomi
AU - Maddalena Ferragatta
AU - Valentina Forini
PY - 2026
DA - 2026/10/19
PB - HAL
DO - 10.48550/arxiv.2610.10723
UR - https://hal.science/hal-05835178v1
AB - We study two-point functions of chiral primary operators in š¯’©=4 Super Yang-Mills in the presence of a half-BPS surface defect. Such a defect preserves only the diagonal combination of transverse rotations and of a global U(1) R-symmetry, so that the correlator depends on one additional cross-ratio and splits into sectors of definite angular charge. We solve the superconformal Ward identities and construct the bulk and defect superconformal blocks in all sectors, including the charged ones, which have no analogue for defects preserving transverse rotations. The solution contains a holomorphic sector, which we fix non-perturbatively by mapping it to a chiral algebra correlator. We extend this map to defects breaking transverse rotations, where it requires a redefinition of the modes of the two-dimensional current algebra, and use it to fix the charged sectors as well. We then use the defect dispersion relation to reconstruct the full correlator of the dimension-two chiral primary at leading order at large N and strong coupling. In the charged sectors long multiplets are absent and the answer is conjecturally exact in both N and the coupling; expanding it at weak coupling, we find perfect agreement with known results. From these correlators we extract infinitely many new pieces of defect CFT data. Finally, we reproduce the strong-coupling answer by an independent Witten diagram bootstrap on the rotation-invariant locus.
ER -