Michael R. Douglas

Bio: Michael R. Douglas is an academic researcher from Rutgers University. The author has contributed to research in topics: Compactification (physics) & Calabi–Yau manifold. The author has an hindex of 39, co-authored 69 publications receiving 7419 citations. Previous affiliations of Michael R. Douglas include Isaac Newton Institute & Stony Brook University.

Noncommutative Geometry and Matrix Theory: Compactification on Tori

Abstract: 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 introduction for mathematicians to the IKKT formulation of Matrix theory and its relation to the BFSS Matrix theory.

On D=5 super Yang-Mills theory and (2,0) theory

Abstract: We discuss how D = 5 maximally supersymmetric Yang-Mills theory (MSYM) might be used to study or even to define the (2, 0) theory in six dimensions. It is known that the compactification of (2, 0) theory on a circle leads to D = 5 MSYM. A variety of arguments suggest that the relation can be reversed, and that all of the degrees of freedom of (2, 0) theory are already present in D = 5 MSYM. If so, this relation should have consequences for D = 5 SYM perturbation theory. We explore whether it might imply all orders finiteness, or else an unusual relation between the cutoff and the gauge coupling. S-duality of the reduction to D = 4 may provide nonperturbative constraints or tests of these options.

A New Hat For The c=1 Matrix Model

Abstract: We consider two dimensional supergravity coupled to $\hat c=1$ matter. This system can also be interpreted as noncritical type 0 string theory in a two dimensional target space. After reviewing and extending the traditional descriptions of this class of theories, we provide a matrix model description. The 0B theory is similar to the realization of two dimensional bosonic string theory via matrix quantum mechanics in an inverted harmonic oscillator potential; the difference is that we expand around a non-perturbatively stable vacuum, where the matrix eigenvalues are equally distributed on both sides of the potential. The 0A theory is described by a quiver matrix model.

String theory and noncommutative geometry

Abstract: We extend earlier ideas about the appearance of noncommutative geometry in string theory with a nonzero B-field. We identify a limit in which the entire string dynamics is described by a minimally coupled (supersymmetric) gauge theory on a noncommutative space, and discuss the corrections away from this limit. Our analysis leads us to an equivalence between ordinary gauge fields and noncommutative gauge fields, which is realized by a change of variables that can be described explicitly. This change of variables is checked by comparing the ordinary Dirac-Born-Infeld theory with its noncommutative counterpart. We obtain a new perspective on noncommutative gauge theory on a torus, its T-duality, and Morita equivalence. We also discuss the D0/D4 system, the relation to M-theory in DLCQ, and a possible noncommutative version of the six-dimensional (2,0) theory.

M theory as a matrix model: A conjecture

Abstract: We suggest and motivate a precise equivalence between uncompactified 11-dimensional $M$ theory and the $N=\ensuremath{\infty}$ 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.

Supergravity and a confining gauge theory: duality cascades and χSB-resolution of naked singularities

Abstract: We revisit the singular IIB supergravity solution describing M fractional 3branes on the conifold [hep-th/0002159]. Its 5-form flux decreases, which we explain by showing that the relevant N = 1 SUSY SU(N+M)×SU(N) gauge theory undergoes repeated Seiberg-duality transformations in which N → N − M. Far in the IR the gauge theory confines; its chiral symmetry breaking removes the singularity of hep-th/0002159 by deforming the conifold. We propose a non-singular pure-supergravity background dual to the field theory on all scales, with small curvature everywhere if the ‘t Hooft coupling gsM is large. In the UV it approaches that of hep-th/0002159, incorporating the logarithmic flow of couplings. In the IR the deformation of the conifold gives a geometrical realization of chiral symmetry breaking and confinement. We suggest that pure N = 1 Yang-Mills may be dual to strings propagating at small gsM on a warped deformed conifold. We note also that the standard model itself may lie at the base of a duality cascade.

Noncommutative field theory

Abstract: This article reviews 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 qualitatively new phenomena have been discovered, on both the classical and the quantum level.