Coupling Self-Dual p-Form Gauge Fields to Self-Dual Branes

In $d=4k+2$ dimensions, $p$-form gauge fields (with $p=2k$) with self-dual field strengths couple naturally to dyonic branes with equal electric and magnetic charges. Sen's action for a $p$-form gauge field with self-dual field strength coupled to a spacetime metric $g$ involves an explicit Minkowski metric; however, this action can be generalised to provide a theory in which the Minkowski metric is replaced by a second metric $\bar g$ on spacetime. This theory describes a physical sector, consisting of the chiral $p$-form gauge field coupled to the dynamical metric $g$, plus an auxiliary sector consisting of a second chiral $p$-form and the second metric $\bar g$. The fields in this auxiliary sector only couple to each other and have no interactions with the physical sector. However, in this theory, the standard coupling to a brane given by integrating the gauge potential over the world-volume of the brane is problematic as the physical gauge potential depends non-locally on the fields appearing in the action. A consistent coupling is given by introducing Dirac branes (generalising Dirac strings), and is shown to have generalised symmetries corresponding to invariance under deforming the positions of the Dirac branes, provided the Dirac branes do not intersect any physical brane world-volumes.