Matrix Theory and U-Duality in Seven Dimensions

TL;DR

This work investigates whether Matrix theory can realize M-theory's U-duality in seven dimensions by compactifying on $T^4$ to obtain a $4+1$-dimensional theory with $N=2$ supersymmetry. The authors promote the gauge-theory parameters to a 5-torus base space, introducing $S_5=g^2$ to reveal an $SL(5,Z)$ classical symmetry and interpret instantons as momentum along an emergent extra dimension, leading to a $5+1$-dimensional description. Supporting evidence from Type IIA string theory shows that strong coupling yields the $(2,0)$ theory on coincident M5-branes, with bound states of $n$ 0-branes and 4-branes aligning with wrapped brane intuition and T-duality. The conclusions organize how wrapped branes and light toron/membrane states expand the Matrix theory base space, suggesting a consistent realization of U-duality and guiding future compactifications and anomaly considerations in the 7D case.

Abstract

We demonstrate the emergence of the U-duality group in compactification of Matrix theory on a 4-torus. The discussion involves non-trivial effects in strongly coupled 4+1 dimensional gauge theory, and highlights some interesting phenomena in the Matrix theory description of compactified M-theory.