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M(atrix) Theory
In physics, M(atrix) theory (also known as BFSS-Matrix theory) is a fundamental formulation of M-theory as a Random matrix model. It is written in terms of interacting D0-branes (zero-dimensional Dirichlet branes) in infinite momentum frame. It was proposed by Banks, Fishler, Shenker, and Susskind in 1996 [1]. See also the discussion in M-theory.
Matrix String Theory
matrix string theory is a set of equations that describe superstring theory in a non-perturbative framework. Matrix string theory is related to M(atrix) theory in the same sense that superstring theory is related to M-theory. 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 [2] and later independently in a more complete paper by Robbert Dijkgraaf, Erik Verlinde, and Herman Verlinde [3]. Another matrix string theory equivalent to Type IIB string theory was constructed in 1996 by Ishibashi, Kawai, Kitazawa and Tsuchiya [4]. This version is known as the IKKT matrix model.
References
[1] T. Banks, W. Fischler, S.H. Shenker and L. Susskind, "M Theory As A Matrix Model: A Conjecture". Phys. Rev. D55 (1997). ar?iv:hep-th/9610043.
[2] L Motl, "Proposals on nonperturbative superstring interactions". ar?iv:hep-th/9701025.
[3] R. Dijkgraaf, E. Verlinde, H. Verlinde, "Matrix String Theory", Nucl. Phys. B 500, p 43 (1997)ar?iv:hep-th/9703030.
[4] N. Ishibashi, H. Kawai, Y.Kitazawa, A. Tsuchiya, "A large-N reduced model as superstring", Nucl. Phys. B 498 (19970 467 ar?iv:hep-th/9612115.
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