Defect conformal field theories with free-in-the-bulk fermions

Abstract

We study codimension-two conformal defects for massless fermions that are free in a four-dimensional bulk, but interact on a two-dimensional defect. The bulk Dirac equation strongly constrains defect conformal field theory data: it fixes the dimensions of operators in the bulk-defect operator product expansion and, for bulk-defect-defect three-point functions, enforces a double-twist relation when only one member of a shadow pair is allowed by unitarity. The lowest modes of monodromy defects provide an important exception, since both shadow partners can be unitary and their three-point functions are instead related by a shadow transform. We illustrate these structures with defect interactions, including an exactly tractable bilinear flow and Gross-Neveu-type quartic couplings. At a perturbative mixed fixed point, we find an explicit interacting example in which the double-twist condition is violated and the two shadow channels combine to give a regular bulk-defect-defect correlation function.