Conic D-branes

The shape of D-branes is of fundamental interest in string theory. We find that, generically, D-branes in trivial spacetime can form a conic shape under external uniform forces. Surprisingly, the apex angle is found to be unique, once the spatial dimensions of the cone are given. In particular, it is universal irrespective of the external forces. The quantized angle is reminiscent of the Taylor cones of hydrodynamic electrospray. We provide explicit D-brane solutions as well as the mechanism of a force balance on the cone, for D-branes in Ramond-Ramond and Neveu-Schwarz-Neveu-Schwarz flux backgrounds. Critical embedding of probe D-branes in anti-de Sitter/conformal field theory with electric and magnetic fields is in the same category, for which we give an analytic proof of a power-law spectrum of "turbulent meson condensation".