Crosscap defects

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

. 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.