PROGRESS IN FOUR-DIMENSIONAL LATTICE SUPERSYMMETRY

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M Theory As A Matrix Model: A Conjecture

L. Susskind, W. Fischler, S. Shenker … (1996)

We suggest and motivate a precise equivalence between uncompactified eleven dimensional M-theory and the N = infinity limit of the supersymmetric matrix quantum mechanics describing D0-branes. The evidence for the conjecture consists of several correspondences between the two theories. As a consequence of supersymmetry the simple matrix model is rich enough to describe the properties of the entire Fock space of massless well separated particles of the supergravity theory. In one particular kinematic situation the leading large distance interaction of these particles is exactly described by supergravity . The model appears to be a nonperturbative realization of the holographic principle. The membrane states required by M-theory are contained as excitations of the matrix model. The membrane world volume is a noncommutative geometry embedded in a noncommutative spacetime.

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A remnant of chiral symmetry on the lattice

Paul Ginsparg, Kenneth G. Wilson (1982)

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Gauge Theory Correlators from Non-Critical String Theory

I. Klebanov, S. S. Gubser, A. M. POLYAKOV (1998)

We suggest a means of obtaining certain Green's functions in 3+1-dimensional \({\cal N} = 4\) supersymmetric Yang-Mills theory with a large number of colors via non-critical string theory. The non-critical string theory is related to critical string theory in anti-deSitter background. We introduce a boundary of the anti-deSitter space analogous to a cut-off on the Liouville coordinate of the two-dimensional string theory. Correlation functions of operators in the gauge theory are related to the dependence of the supergravity action on the boundary conditions. From the quadratic terms in supergravity we read off the anomalous dimensions. For operators that couple to massless string states it has been established through absorption calculations that the anomalous dimensions vanish, and we rederive this result. The operators that couple to massive string states at level \(n\) acquire anomalous dimensions that grow as \(2\left (n g_{YM} \sqrt {2 N} )^{1/2}\) for large `t Hooft coupling. This is a new prediction about the strong coupling behavior of large \(N\) SYM theory.