Anomalies and large N limits in matrix string theory

We study the loop expansion for the low energy effective action for matrix string theory. For long string configurations we find the result depends on the ordering of limits. Taking $g_s\to 0$ before $N\to\infty$ we find free strings. Reversing the order of limits however we find anomalous contributions coming from the large $N$ limit that invalidate the loop expansion. We then embed the classical instanton solution into a long string configuration. We find the instanton has a loop expansion weighted by fractional powers of $N$. Finally we identify the scaling regime for which interacting long string configurations have a well defined large $N$ limit. The limit corresponds to large "classical" strings and can be identified with the "dual of the 't Hooft limit, $g_{SYM}^2\sim N$.Comment: 13 pages, 1 figure, harvmac.tex, notational errors corrected, references added. Trivial error in section 5 corrected with the result that the domain of validity of the loop expn. is slightly modifie

BPS Configuration of Supermembrane With Winding in M-direction

We study de Wit-Hoppe-Nicolai supermembrane with emphasis on the winding in M-direction. We propose a SUSY algebra of the supermembrane in the Lorentz invariant form. We analyze the BPS conditions and argue that the area preserving diffeomorphism constraints associated with the harmonic vector fields play an essential role. We derive the first order partial differential equation that describes the BPS state with one quarter SUSY.Comment: 10 pages latex, references adde

Membrane Scattering in Curved Space with M-Momentum Transfer

We study membrane scattering in a curved space with non-zero M-momentum p_{11} transfer. In the low-energy short-distance region, the membrane dynamics is described by a three-dimensional N=4 supersymmetric gauge theory. We study an n-instanton process of the gauge theory, corresponding to the exchange of n units of p_{11}, and compare the result with the scattering amplitude computed in the low-energy long-distance region using supergravity. We find that they behave differently. We show that this result is not in contradiction with the large-N Matrix Theory conjecture, by pointing out that cutoff scales of the supergravity and the gauge theory are complementary to each other.Comment: 30 pages, 2 postscript figures, late

Topological Inflation in Dual Superstring Models

We study the possibility of obtaining inflationary solutions from S-dual superstring potentials. We find, in particular, that such solutions occur at the core of domain walls separating degenerate minima whose positions differ by modular transformations.Comment: 12 pages, uuencoded gzipped tar format, Latex, 2 figure

M-Branes and Their Interactions in Static Matrix Model

Different BPS M-brane configurations including single and two parallel M$p$-branes ($p$= even) and M5-branes are introduced as the classical solutions of the recently proposed Static Matrix Model. Also the long range interactions of two relatively rotated M$p$-branes (one and two angles) and M$p$-brane--anti-M$p$-brane are calculated. The results are in agreement with 11 dimensional supergravity results.Comment: Latex file, 17 pages, No Figure

D0-branes in an H-field Background and Noncommutative Geometry

It is known that if we compactify D0-branes on a torus with constant B-field, the resulting theory becomes SYM theory on a noncommutative dual torus. We discuss the extension to the case of a H-field background. In the case of constant H-field on a three-torus, we derive the constraints to realize this compactification by considering the correspondence to string theory. We carry out this work as a first step to examine the possibility to describe transverse M5-branes in Matrix theory.Comment: 15 pages, LaTeX; some comments added, typos corrected, to appear in Nucl. Phys.

Born-Infeld Actions from Matrix Theory

We propose a formula for the effective action of Matrix Theory which succesfully reproduces a large class of Born-Infeld type D-brane probe actions. The formula is motivated by demanding consistency with known results, and is tested by comparing with a wide range of source-probe calculations in supergravity. In the case of D0-brane sources and Dp-brane probes, we study the effect of boosts, rotations, and worldvolume electric fields on the probe, and find agreement with supergravity to all orders in the gravitational coupling. We also consider D4-brane sources at the one loop level and recover the correct probe actions for a D0-brane, and for a D4-brane rotated at an angle with respect to the source.Comment: 27 pages, LaTeX fil

Gaugino Condensation, Duality and Supersymmetry Breaking

The status of gaugino condensation in low-energy string theory is reviewed. Emphasis is given to the determination of the efective action below condensation scale in terms of the 2PI and Wilson actions. We illustrate how the different perturbative duality symmetries survive this simple nonperturbative phenomenon, providing evidence for the believe that these are exact nonperturbative symmetries of string theory. Consistency with T duality lifts the moduli degeneracy. The $B_{\mu\nu}-axion$ duality also survives in a nontrivial way in which the degree of freedom corresponding to $B_{\mu\nu}$ is replaced by a massive $H_{\mu\nu\rho}$ field but duality is preserved. S duality may also be implemented in this process. Some general problems of this mechanism are mentioned and the possible nonperturbative scenarios for supersymmetry breaking in string theory are discussed.Comment: Contribution to Trieste Conference on S-Duality and Mirror Symmetry, 20 pages. Late

The Problem of the Stabilization of the Dilaton in String Theories

The crucial problem of how the dilaton field is stabilized at a phenomenologically acceptable value in string theories remains essentially unsolved. We show that the usual scenario of assuming that the dilaton is fixed by the (SUSY breaking) dynamics of just the dilaton itself (dilaton dominance scenario) is {\em inconsistent} unless the K\"ahler potential receives very important perturbative or non-perturbative contributions. Then, the usual predictions about soft breaking terms are lost, but still is possible to derive model-independent predictions for them.Comment: 7 pages, LaTeX. Talk given at SUSY-96, Univ. of Maryland, College Park, May 29 - June 1, 199

D-branes and Matrix Theory in Curved Space

We discuss the relation between supersymmetric gauge theory of branes and supergravity; as it was discovered in D-brane physics, and as it appears in Matrix theory, with emphasis on motion in curved backgrounds. We argue that gauged sigma model Lagrangians can be used as definitions of Matrix theory in curved space. Lecture given at Strings '97; June 20, 1997.Comment: LaTeX with espcrc2; 13 pages, STRINGS97. References added; a speculation refute