T - DUALITY OF p - BRANES

We investigate possible existence of duality symmetries which exchange the Kaluza-Klein modes with the wrapping modes of a BPS saturated p-brane on a torus. Assuming the validity of the conjectured U-duality symmetries of type II and heterotic string theories and M-theory, we show that for a BPS saturated p-brane there is an SL(2,Z) symmetry that mixes the Kaluza-Klein modes on a (p+1) dimensional torus T (p+1) with the wrapping modes of the p-brane on T (p+1). The field that transforms as a modular parameter under this SL(2,Z) transformation has as its real part the component of the (p + 1)-form gauge field on T (p+1) , and as its imaginary part the volume of T (p+1) , measured in the metric that couples naturally to the p-brane.