Positronium-like states from supergravity

We study semi-classical rotating open strings ending on a probe Dp-brane close to a stack of extremal, non-extremal Dp-branes and Dp-branes with $B$-fields. These states may be interpreted as positronium-like bound states of spinning W-bosons in an $SU(N+1)\to SU(N)\times U(1)$ theory. In each case, we describe the behaviour of the strings and examine the relation between the energy and the angular momentum of the bound state.