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We study toroidal compactification of Matrix theory, using ideas and results of non-commutative geometry. We generalize this to compactification on the noncommutative torus, explain the classification of these backgrounds, and argue that they correspond in supergravity to tori with constant background three-form tensor field. The paper includes an(More)
Motivated by recent work of Dijkgraaf and Vafa, we study anomalies and the chiral ring structure in a supersymmetric U (N) gauge theory with an adjoint chiral superfield and an arbitrary superpotential. A certain generalization of the Konishi anomaly leads to an equation which is identical to the loop equation of a bosonic matrix model. This allows us to(More)
We review the generalization of field theory to space-time with noncommuting coordinates, starting with the basics and covering most of the active directions of research. Such theories are now known to emerge from limits of M theory and string theory, and to describe quantum Hall states. In the last few years they have been studied intensively, and many(More)
We show that in certain superstring compactifications, gauge theories on noncom-mutative tori will naturally appear as D-brane world-volume theories. This gives strong evidence that they are well-defined quantum theories. It also gives a physical derivation of the identification proposed by Connes, Douglas and Schwarz of Matrix theory com-pactification on(More)
We show that configurations of multiple D-branes related by SU (N) rotations will preserve unbroken supersymmetry. This includes cases in which two D-branes are related by a rotation of arbitrarily small angle, and we discuss some of the physics of this. In particular, we discuss a way of obtaining 4D chiral fermions on the intersection of D-branes. We also(More)
We study the behavior of D-branes at distances far shorter than the string length scale l s. We argue that short-distance phenomena are described by the IR behavior of the D-brane world-volume quantum theory. This description is valid until the brane motion becomes relativistic. At weak string coupling g s this corresponds to momenta and energies far above(More)
We study D-branes on the quintic CY by combining results from several directions: general results on holomorphic curves and vector bundles, stringy geometry and mirror symmetry, and the boundary states in Gepner models recently constructed by Recknagel and Schome-rus, to begin sketching a picture of D-branes in the stringy regime. We also make first steps(More)
We establish that the open string star product in the zero momentum sector can be described as a continuous tensor product of mutually commuting two dimensional Moyal star products. Let the continuous variable κ ∈ [ 0, ∞) parametrize the eigenvalues of the Neumann matrices; then the noncommutativity parameter is given by θ(κ) = 2 tanh(πκ 4). For each κ, the(More)
We study the physics of the Seiberg-Witten and Argyres-Faraggi-Klemm-Lerche-Theisen-Yankielowicz solutions of D = 4, N = 2 and N = 1 SU (N) supersymmetric gauge theory. The N = 1 theory is confining and its effective Lagrangian is a spontaneously broken U (1) N−1 abelian gauge theory. We identify some features of its physics which see this internal(More)
We study topological properties of the D-brane resolution of three-dimensional orbifold singularities, C 3 /Γ, for finite abelian groups Γ. The D-brane vacuum moduli space is shown to fill out the background spacetime with Fayet–Iliopoulos parameters controlling the size of the blow-ups. This D-brane vacuum moduli space can be classically described by a(More)