Topological Matrix Model

Starting from the primal principle based on the noncommutative nature of (9+1)-dimensional spacetime, we construct a topologically twisted version of the supersymmetric reduced model with a certain modification. Our formulation automatically provides extra 1+1 dimensions, thereby the dimensions of spacetime are promoted to 10+2. With a suitable gauge choice, we can reduce the model with (10+2)-dimensional spacetime to the one with (9+1)-dimensions and thus we regard this gauge as the light-cone gauge. It is suggested that the model so obtained would describe the light-cone F-theory. From this viewpoint we argue the relation of the reduced model to the matrix model of M-theory and the SL(2,Z) symmetry of type IIB string theory. We also discuss the general covariance of the matrix model in a broken phase, and make some comments on the background independence.Comment: 18 pages, LaTeX, no figures, minor corrections and modifications, references adde

Matrix model with superconformal symmetry

A matrix model is presented which leads to the discrete ``eigenvalue model'' proposed recently by Alvarez-Gaum\'e {\it et.al.} for 2D supergravity (coupled to superconformal matters).Comment: 7p

Little IIB Matrix Model

We study the zero-dimensional reduced model of D=6 pure super Yang-Mills theory and argue that the large N limit describes the (2,0) Little String Theory. The one-loop effective action shows that the force exerted between two diagonal blocks of matrices behaves as 1/r^4, implying a six-dimensional spacetime. We also observe that it is due to non-gravitational interactions. We construct wave functions and vertex operators which realize the D=6, (2,0) tensor representation. We also comment on other "little" analogues of the IIB matrix model and Matrix Theory with less supercharges.Comment: 17 pages, references adde

A Matrix Model Black Hole

In this paper the $c=1$ matrix model deformed by a $1/x^{2}$ piece is discussed. Tachyon correlation functions are calculated up to genus two using methods similar to those for the undeformed case. The possible connection with the two dimensional black hole is also considered. In particular, restrictions on naked singularities imposed by the matrix model are found.Comment: 15 pages, Latex, 2 figures available on request, CERN-TH.6916/93. Minor typos correcte

A Matrix Model for AdS2

A matrix quantum mechanics with potential $V={q^2 \over r^2}$ and an SL(2,R) conformal symmetry is conjectured to be dual to two-dimensional type 0A string theory on AdS$_2$ with $q$ units of RR flux.Comment: 12 page

Maxwell Theory from Matrix Model

We present a scenario for deriving Maxwell theory from IIB matrix model. Four dimensional spacetime and theories on it relate different dimensional ones by applying appropriate limits of the backgrounds of matrix model. It is understood by looking at open strings bits as bi-local fields on the spacetime, which are decoupled from the bulk in the limits. The origin of electric-magnetic duality is also discussed in matrix model.Comment: Lattice 2000 (Gravity and Matrix Models), 4 page

The Cauchy two-matrix model

We introduce a new class of two(multi)-matrix models of positive Hermitean matrices coupled in a chain; the coupling is related to the Cauchy kernel and differs from the exponential coupling more commonly used in similar models. The correlation functions are expressed entirely in terms of certain biorthogonal polynomials and solutions of appropriate Riemann-Hilbert problems, thus paving the way to a steepest descent analysis and universality results. The interpretation of the formal expansion of the partition function in terms of multicolored ribbon-graphs is provided and a connection to the O(1) model. A steepest descent analysis of the partition function reveals that the model is related to a trigonal curve (three-sheeted covering of the plane) much in the same way as the Hermitean matrix model is related to a hyperelliptic curve.Comment: 34 pages, 2 figures. V2: changes only to metadat

Why is the Matrix Model Correct?

We consider the compactification of M theory on a light-like circle as a limit of a compactification on a small spatial circle boosted by a large amount. Assuming that the compactification on a small spatial circle is weakly coupled type IIA theory, we derive Susskind's conjecture that M theory compactified on a light-like circle is given by the finite $N$ version of the Matrix model of Banks, Fischler, Shenker and Susskind. This point of view provides a uniform derivation of the Matrix model for M theory compactified on a transverse torus $T^p$ for $p=0,...,5$ and clarifies the difficulties for larger values of $p$.Comment: 9 page