Würzburg Seminar on Quantum Field Theory and Gravity (Daniel Lloyd-Jones, 03.11.2026)

Defect and boundary conformal field theories provide a conceptual foundation for many topics in theoretical physics, from critical systems in condensed matter, to entanglement phenomena in many-body physics, to D-branes in string theory. I will talk about a computationally tractable yet still physically relevant subset, where the bulk is free and gapless, and the interactions are confined to the defect or boundary. In these theories, the free bulk equation of motion 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. If both shadow partners can be unitary then their three-point functions are instead related by a shadow transform. I will focus on free-in-the-bulk fermions and illustrate these effects by looking at specific interacting theories.