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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 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 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 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)