Bootstrapping boundaries and branes

A bstract The study of conformal boundary conditions for two-dimensional field theories (CFTs) has a long history, ranging from the description impurities in one-dimensional quantum chains to formulation D-branes string theory. Nevertheless, landscape boundaries is largely unknown, including rational CFTs, where local operator data completely determined. We initiate systematic bootstrap 2d CFTs by investigating equation that arises open-closed consistency condition annulus partition function with identical boundaries. find this deceivingly simple equation, when combined unitarity, leads surprisingly strong constraints on admissible states. In particular, we derive universal bounds tension (boundary entropy) stable conditions, which provide rigorous diagnostic potential D-brane decays. also unique solutions problem branes number CFTs. Along way, observe curious connection between and sphere packing problem, natural extension previous work modular bootstrap. entropy at large central charge. These potentially have implications end-of-the-world pure gravity AdS 3 .