Non-Commutative Geometry from Strings

To appear in Encyclopedia of Mathematical Physics, J.-P. Fran\c{c}oise, G. Naber and T.S. Tsou, eds., Elsevier, 2006. The article surveys the modern developments of noncommutative geometry in string theory.Comment: 26 pages, no figures. To appear in the Elsevier Encyclopedia of Mathematical Physics. This web version has a more comprehensive list of references. Comments and corrections welcome. v2: Typos corrected, references and some comments added. v3: 27 pages. more references and Comments added. v4: references added. Final versio

On Non-Abelian Structure From Matrix Coordinates

We consider the matrix quantum mechanics of N D0-branes in the background of the 1-form RR field. It is observed that the transformations of matrix coordinates of D0-branes induce on the Abelian RR field symmetry transformations that are like those of non-Abelian gauge fields. The Lorentz-like equations of motion for matrix coordinates are derived. The field strengths appearing in the Lorentz-like equations transform in the adjoint representation of U(N) under symmetry transformations. A possible relation between D0-brane dynamics in RR background, and the semi-classical dynamics of charged particles in Yang-Mills background is mentioned.Comment: 12 pages, no figures, LaTeX. v2: typos fixed, to appear in Phys. Lett.

Matrix Strings in Weakly Curved Background Fields

We investigate further the recent proposal for the form of the Matrix theory action in weak background fields. We perform DVV reduction to the multiple D0-brane action in order to find the Matrix string theory action for multiple fundamental strings in curved but weak NS-NS and R-R backgrounds. This matrix sigma model gives a definite prescription on how to deal with R-R fields with an explicit spacetime dependence in Type II string theory. We do this both via the 9-11 flip and the chain of T and S dualities, and further check on their equivalence explicitly. In order to do so, we also discuss the implementation of S-duality in the operators of the 2-dimensional world-volume supersymmetric gauge theory describing the Type IIB D-string. We compare the result to the known Green-Schwarz sigma model action (for one string), and use this comparison in order to discuss about possible, non-linear background curvature corrections to the Matrix string action (involving many strings), and therefore to the Matrix theory action. We illustrate the nonabelian character of our action with an example involving multiple fundamental strings in a non-trivial R-R flux, where the strings are polarized into a noncommutative configuration. This corresponds to a dielectric type of effect on fundamental strings.Comment: 46 pages, Latex; v2: added 3 refs and 1 commen

Evidence for a gravitational Myers effect

An indication for the existence of a collective Myers solution in the non-abelian D0-brane Born-Infeld action is the presence of a tachyonic mode in fluctuations around the standard diagonal background. We show that this computation for non-abelian D0-branes in curved space has the geometric interpretation of computing the eigenvalues of the geodesic deviation operator for U(N)-valued coordinates. On general grounds one therefore expects a geometric Myers effect in regions of sufficiently negative curvature. We confirm this by explicit computations for non-abelian D0-branes on a sphere and a hyperboloid. For the former the diagonal solution is stable, but not so for the latter. We conclude by showing that near the horizon of a Schwarzschild black hole one also finds a tachyonic mode in the fluctuation spectrum, signaling the possibility of a near-horizon gravitationally induced Myers effect.Comment: LaTeX, 23 page

THE INFLUENCE OF TECHNOLOGICAL PROGRESS ON THE LONG RUN FARM LEVEL ECONOMICS OF SOIL CONSERVATION

The complementary interaction between topsoil depth and technical progress for winter wheat in the Palouse region was found to strengthen the long run payoff to conservation tillage. Nonetheless, conservation tillage was found to be competitive with conventional tillage only if its current yield disadvantages were eliminated. Conservation tillage was relatively more competitive on shallower topsoils and for longer planning horizons. Short-term subsidies coupled with research directed towards reducing the cost and yield disadvantages of conservation tillage in the Palouse were advocated to maintain long-term soil productivity.Land Economics/Use, Research and Development/Tech Change/Emerging Technologies,

Issues in M(atrix) Theory Compactification

We discuss issues concerning M(atrix) theory compactifications on curved spaces. We argue from the form of the graviton propagator on curved space that excited string states do not decouple from the annulus D0-brane $v^4$ amplitude, unlike the flat space case. This argument shows that a large class of quantum mechanical systems with a finite number of degrees of freedom cannot reproduce supergravity answers. We discuss the specific example of an ALE space and suggest sources of possible higher derivative terms that might help reproduce supergravity results.Comment: title modified, references corrected, 11 pages, harvma