Spinning conformal defects

Abstract

We consider conformal defects with spins under the rotation group acting on the transverse directions. They are described in the embedding space formalism in a similar manner to spinning local operators, and their correlation functions with bulk and defect local operators are determined by the conformal symmetry. The operator product expansion (OPE) structure of spinning conformal defects is examined by decomposing it into the spinning defect OPE block that packages all the contribution from a conformal multiplet. The integral representation of the block derived in the shadow formalism is facilitated to deduce recursion relations for correlation functions of two spinning conformal defects. In simple cases, we construct spinning defect correlators by acting differential operators recursively on scalar defect correlators. Discussion 30A Identities 32 B Shadow operator 32 -1 -

Line and surface defects for the free scalar field

“…If we now put the p-dimensional defect on an R p subspace of R d then we can assume that it preserves: (a) a p-dimensional Poincaré symmetry, (b) rotations in the transverse d − p dimensions, and (c) an overall dilatation symmetry in the infrared. There are exceptions to (a) and (b), see for example [1] for the kinematics of defects charged under transverse rotations, but we will not consider this here. As for (c), a simple computation involving the bulk stress tensor shows that this scale invariance is enhanced to so(p + 1, 1), so pdimensional conformal invariance, if the defect does not contain a specific 'virial current' of dimension p − 1, see for example [2].…”

Calogero-Sutherland approach to defect blocks

“…In order to explore the features of these new functions, understand their analytical properties or find useful expansions one could try to follow the same route that was used for four-point blocks, see e.g. [29,30] for some recent work in this direction. It is the central message of this paper, however, that there is another route that gives a much more direct access to defect blocks.…”

Bootstrapping the half-BPS line defect

“…We should also mention that, as opposed to local operators in the presence of a defect, one can also study correlation functions of the defects themselves. Works in this direction include [20][21][22].…”