Equations of Motion and Galilei Invariance in D-Particle Dynamics

As a continuation of our previous work on the multi-body forces of D-particles in supergravity and Matrix theory, we investigate the problem of motion. We show that the scattering of D-particles including recoil derived in Matrix theory is precisely reproduced by supergravity with the discrete light-cone prescription up to the second order in 11 dimensional Newton constant. An intimate connection of recoil and Galilei invariance in supergravity is pointed out and elucidated.Comment: 19 pages, no figures, LaTe

Three-graviton scattering in Matrix theory revisited

We consider a subset of the terms in the effective potential describing three-graviton interactions in Matrix theory and in classical eleven-dimensional supergravity. In agreement with the results of Dine and Rajaraman, we find that these terms vanish in Matrix theory. We show that the absence of these terms is compatible with the classical supergravity theory when the theory is compactified in a lightlike direction, resolving an apparent discrepancy between the two theories. A brief discussion is given of how this calculation might be generalized to compare the Matrix theory and supergravity descriptions of an arbitrary 3-body system.Comment: 9 pages, LaTeX; v2: reference added, v3: text unchanged, Note added clarifying connection with other recent result

A Note on Fluxes in Six-Dimensional String Theory Backgrounds

We study the structure of warped compactifications of type IIB string theory to six space-time dimensions. We find that the most general four-manifold describing the internal dimensions is conformal to a Kahler manifold, in contrast with the heterotic case where the four-manifold must be conformally Calabi-Yau.Comment: 22 pages, phyzz

Long-term effects of timber management on forest breeding songbirds in the central Appalachians

I conducted 50-m fixed radius point counts and monitored nests at the Wildlife and Ecosystem Research Forest (WERF) and Panther Run Tract in Randolph County, WV, from 2007--2009 and incorporated previous research using the same techniques from 1996--1998 and 2001--2003.;In chapter two, my objectives were to identify temporal abundance and nest success trends and identify landscape-scale disturbance thresholds for species and habitat guilds using a variety of harvests. Early successional species increased in relative abundance, while interior-edge and forest-interior guilds peaked in relative abundance mid-study, after which the forest-interior guild declined. Of 44 analyzed species, 9% declined, 36% increased, and 32% peaked in abundance mid-study. Forest-interior and interior-edge guilds exhibited thresholds, a disproportionate response in bird abundance relative to a small change in habitat results, at 28% of the landscape, 10% harvesting by clear-cuts, and 18% harvesting by light partial harvests, after which abundances declined. Thresholds for the early successional guild were greater for total harvests (42%), similar for harvesting by clear-cuts (11%), and smaller for light partial harvests(10%), for which relative abundances increased after surpassing thresholds except for a reduction in the rate of increase for clear-cuts. Even though abundance of most species (82%) did not decline as the area affected by timber management increased, implementing management at or below our approximate harvest thresholds for forest-interior and interior-edge guilds would reduce the number of declining species by half.;In chapter three, my objective was to use the broader spectrum of habitat conditions resulting from long-term management to categorize bird species into habitat groups, identify habitat commonalities between group members, and determine habitat conditions associated with successful nests. Using non-metric multidimensional scaling (NMDS), I identified four habitat groups: mature forest, disturbed-canopy low elevation, disturbed-canopy high elevation, and early succession. Early successional species increased in abundance with greater amount of clear-cuts, heavy partial harvests, and edge density. The two disturbed-canopy groups (divided based on elevation) had no consistent metrics among species, but included variables representing different aspects of disturbed mature forests. Mature (undisturbed) forest species declined in abundance with increased clear-cuts, core early succession habitat, and habitat intermixing and reduced shape complexity. Nest success models had high error due to small sample sizes; still, they suggested different conditions are required for successful breeding than for high abundance. My results highlight the need to reconsider the classification of bird species with respect to habitat created by timber management. Group members shared many habitat commonalities and model error was improved over traditional habitat guilds, but variation remains among most species within these groups.;In chapter four, my objectives were to evaluate the response of Canada Warbler (CAWA) abundance and nest success to habitat characteristics as they changed due to forest management practices. According to the Breeding Bird Survey (BBS), the abundance of this declining species has been stable in the Appalachian Bird Conservation Region (BCR), suggesting this region may make important contributions to the species\u27 conservation; however, off-road point count results indicate that CAWA relative abundance decreased on the WERF and the Appalachian BCR, but at lower yearly rates on the WERF. Early in the study, relative abundance was greater closer to roads, but as timber harvest became more common, it was positively related to area of light partial harvests at the local scale. Overall, relative abundance responded positively to all three types of timber harvests. Nest success did not differ between 1996--1998 and 2007--2009. Nests in 2007--2009 had less intermediate canopy cover and residual trees but more green cover, woody debris, and pole trees than nests in 1996--1998. Successful nests had more low cover, less vertical diversity, more woody debris, more saplings, and greater edge density than unsuccessful nests. My research finds preliminary support for use of timber harvests management tool for Canada Warblers in the southern portion of their range with the need for long-term monitoring of abundance and nest success to confirm successful management. (Abstract shortened by UMI.)

Multi-Body Interactions of D-Particles in Supergravity and Matrix Theory

We present detailed analyses of the 3-body interactions of D-particles from both sides of 11 dimensional supergravity and Matrix theory. In supergravity, we derive a complete expression for the classical bosonic effective action for D-particles including 2-and 3-body interaction terms. In Matrix theory, we compute 1-particle irreducible contributions to the eikonal phase shift in the two-loop approximation. The results precisely agree with the predictions from supergravity and thus provide a strong support to the discrete light-cone interpretation of the Matrix-theory conjecture as a possible nonperturbative definition of M-theory.Comment: 38 pages, no figures, a few minor typos are correcte

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

Gauge Theory, Geometry and the Large N Limit

We study the relationship between M theory on a nearly lightlike circle and U(N) gauge theory in p+1 dimensions. We define large N limits of these theories in which low energy supergravity is valid. The regularity of these limits implies an infinite series of nonrenormalization theorems for the gauge theory effective action, and the leading large N terms sum to a Born-Infeld form. Compatibility of two different large N limits that describe the same decompactified M theory leads to a conjecture for a relation between two limits of string theories.Comment: LaTeX, 17 pages, 1 figure, references added, shorter version to appear in Nucl. Phys.

Finite-Time Amplitudes In Matrix Theory

We evaluate one-loop finite-time amplitudes for graviton scattering in Matrix theory and compare to the corresponding amplitudes in supergravity. We find agreement for arbitrary time intervals at leading order in distance, providing a functional agreement between supergravity and Matrix theory. At subleading order, we find corrections to the effective potential found from previous phase shift calculations in Matrix theory.Comment: 12 pages, harvmac, reference added, typo correcte

Non-linear Yang-Mills instantons from strings are π\pi-stable D-branes

We show that B-type $\Pi$-stable D-branes do not in general reduce to the (Gieseker-) stable holomorphic vector bundles used in mathematics to construct moduli spaces. We show that solutions of the almost Hermitian Yang--Mills equations for the non-linear deformations of Yang--Mills instantons that appear in the low-energy geometric limit of strings exist iff they are $\pi$-stable, a geometric large volume version of $\Pi$-stability. This shows that $\pi$-stability is the correct physical stability concept. We speculate that this string-canonical choice of stable objects, which is encoded in and derived from the central charge of the string-\emph{algebra}, should find applications to algebraic geometry where there is no canonical choice of stable \emph{geometrical} objects.Comment: v3: Minor revision; 14 page