In physics, Matrix string theory is a set of equations that describe superstring theory in a non-perturbative framework. Type IIA string theory can be shown to be equivalent to a maximally supersymmetric two-dimensional gauge theory, the gauge group of which is U(N) for a large value of N. This Matrix string theory was first proposed by Luboš Motl in 1997 [1] and later independently in a more complete paper by Robbert Dijkgraaf, Erik Verlinde, and Herman Verlinde.[2] Another matrix string theory equivalent to Type IIB string theory was constructed in 1996 by Ishibashi, Kawai, Kitazawa and Tsuchiya.[3] This version is known as the IKKT matrix model.
M(atrix) theory (also known as BFSS-Matrix theory) is a fundamental formulation of M-theory as a Random matrix model. Matrix string theory is related to M(atrix) theory in the same sense that superstring theory is related to M-theory.
M(atrix) theory is written in terms of interacting D0-branes (zero-dimensional Dirichlet branes) in infinite momentum frame. It was proposed by Banks, Fischler, Shenker, and Susskind in 1996.[4] See also the discussion in M-theory.