Crosscap defects
- 1King’s College London
- 2Department of Theoretical Physics, CERN
- 3Laboratory for Theoretical Fundamental Physics, EPFL
Abstract
A bstract : We introduce a novel class of defects, termed crosscap defects , in conformal field theory (CFT) in general dimensions. These arise from quotienting the spacetime by a ℤ ₂ automorphism, and provide higher-codimension generalisations of CFTs on real projective space (ℝℙd) RP d . Crosscap defects extend along a p -dimensional fixed locus of the ℤ ₂ action and preserve an SO ( p + 1, 1) × PO ( d – p ) subgroup of the conformal group. The two-point functions of operators in this setup exhibit three operator product expansion channels: bulk, image, and defect. These lead to several crosscap crossing equations , which we present. We analyse conformal block decompositions and show that the blocks are identical to defect CFT blocks up to a redefinition of cross ratios. As concrete examples, we study crosscap defects in the O ( N ) model at the Gaussian and Wilson-Fisher fixed points in the ε -expansion. We compute explicitly the associated CFT data as a function of p and find that, unlike standard defects, displacement and tilt operators are absent for generic p . They provide examples of defect conformal manifolds without exactly marginal operators.
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BibTeX
@article{drukker2026crosscap,
title = {{Crosscap defects}},
author = {Nadav Drukker and Shota Komatsu and Anders Wallberg},
journal = {Journal of High Energy Physics},
year = {2026},
month = oct,
doi = {10.1007/jhep10(2026)241},
url = {https://link.springer.com/article/10.1007/JHEP10(2026)241},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Crosscap defects
AU - Nadav Drukker
AU - Shota Komatsu
AU - Anders Wallberg
PY - 2026
DA - 2026/10/23
JO - Journal of High Energy Physics
DO - 10.1007/jhep10(2026)241
UR - https://link.springer.com/article/10.1007/JHEP10(2026)241
AB - A bstract : We introduce a novel class of defects, termed crosscap defects , in conformal field theory (CFT) in general dimensions. These arise from quotienting the spacetime by a ℤ ₂ automorphism, and provide higher-codimension generalisations of CFTs on real projective space (ℝℙ^d) RP d . Crosscap defects extend along a p -dimensional fixed locus of the ℤ ₂ action and preserve an SO ( p + 1, 1) × PO ( d – p ) subgroup of the conformal group. The two-point functions of operators in this setup exhibit three operator product expansion channels: bulk, image, and defect. These lead to several crosscap crossing equations , which we present. We analyse conformal block decompositions and show that the blocks are identical to defect CFT blocks up to a redefinition of cross ratios. As concrete examples, we study crosscap defects in the O ( N ) model at the Gaussian and Wilson-Fisher fixed points in the ε -expansion. We compute explicitly the associated CFT data as a function of p and find that, unlike standard defects, displacement and tilt operators are absent for generic p . They provide examples of defect conformal manifolds without exactly marginal operators.
SN - 1029-8479
ER -