Branes, Fluxes and Duality in M(atrix)-Theory

Abstract

We use the T-duality transformation which relates M-theory on $T^3$ to M-theory on a second $T^3$ with inverse volume to test the Banks-Fischler-Shenker-Susskind suggestion for the Matrix model description of M-theory. We find that T-duality is realized as S-duality for $U(\infty)$ $N=4$ Super-Yang-Mills in 3+1D. We argue that Kaluza-Klein states of gravitons correspond to electric fluxes, wrapped membranes become magnetic fluxes and instantonic membranes are related to Yang-Mills instantons. The T-duality transformation of gravitons into wrapped membranes is interpreted as the S-duality between electric and magnetic fluxes. The transformation of unwrapped membranes into wrapped 5-branes suggests the form of the 5-brane wave function in the matrix model.