U-duality p-Branes in Diverse Dimensions

U-duality p-branes in toroidally compactified type II superstring theories in space-time dimensions 10 > D ≥ 4 can be constructed explicitly based on the conjectured U-duality symmetries and the corresponding known single-charge super p-brane configurations. As concrete examples, we first construct explicitly the SL(3, Z) superstrings and SL(3, Z) × SL(2, Z) 0-branes as well as their corresponding magnetic duals in D = 8. For the SL(3, Z) superstrings (3-branes), each of them is characterized by a triplet of integers corresponding to the electric-like (magnetic-like) charges associated with the three 2-form gauge potentials present in the theory. For the SL(3, Z) × SL(2, Z) 0-branes (4-branes), each of them is labelled by a pair of triplets of integers corresponding to the electric-like (magnetic-like) charges associated with the two sets of three 1-form gauge potentials. The string (3-brane) tension and central charge are shown to be given by SL(3, Z) invariant expressions. It is argued that when any two of the three integers in the integral triplet are relatively prime to each other, the corresponding string (3-brane) is stable and does not decay into multiple strings (3-branes) by a 'tension gap' or 'charge gap' equation. Similar results hold also for the 0-branes (4-branes). Alongwith the SL(2, Z) dyonic membranes of Izquierdo et. al., these examples provide a further support for the conjectured SL(3, Z) × SL(2, Z) U-duality symmetry in this theory. Moreover, the study of these examples along with the previous ones provides us a recipe for constructing the U-duality p-branes of various supergravity theories in diverse dimensions. Constructions for these U-duality p-branes are also given.