An Exact Prediction of N=4 SUSYM Theory for String Theory

We propose that the expectation value of a circular BPS-Wilson loop in N=4 SUSYM can be calculated exactly, to all orders in a 1/N expansion and to all orders in g^2 N. Using the AdS/CFT duality, this result yields a prediction of the value of the string amplitude with a circular boundary to all orders in alpha' and to all orders in g_s. We then compare this result with string theory. We find that the gauge theory calculation, for large g^2 N and to all orders in the 1/N^2 expansion does agree with the leading string theory calculation, to all orders in g_s and to lowest order in alpha'. We also find a relation between the expectation value of any closed smooth Wilson loop and the loop related to it by an inversion that takes a point along the loop to infinity, and compare this result, again successfully, with string theory.Comment: LaTeX, 22 pages, 3 figures. Argument corrected and two new sections adde

Solution of gauge theories induced by fundamental representation scalars

Gauge theories induced by scalars in the fundamental representation of the $U(N_c)_{gauge}\times U(N_f)_{global}$ group are investigated in the large $N_c$ and $N_f$ limit. A master field is defined from bilinears of the scalar field following an Eguchi-Kawai type reduction of spacetime. The density function for the master field satisfies an integral equation that can be solved exactly in two dimensions (D=2) and in a convergent series of approximations at $D>2$. While at D=2 the system is in the same phase at all $\epsilon=N_c/N_f$, it undergoes a phase transition at a critical value, $\epsilon_c(D)$, for $D>2$.Comment: 12 pages, LaTe

Self-interaction effects on screening in three-dimensional QED

We have shown that self interaction effects in massive quantum electrodynamics can lead to the formation of bound states of quark antiquark pairs. A current-current fermion coupling term is introduced, which induces a well in the potential energy profile. Explicit expressions of the effective potential and renormalized parameters are provided

Optimal control of time-dependent targets

In this work, we investigate how and to which extent a quantum system can be driven along a prescribed path in Hilbert space by a suitably shaped laser pulse. To calculate the optimal, i.e., the variationally best pulse, a properly defined functional is maximized. This leads to a monotonically convergent algorithm which is computationally not more expensive than the standard optimal-control techniques to push a system, without specifying the path, from a given initial to a given final state. The method is successfully applied to drive the time-dependent density along a given trajectory in real space and to control the time-dependent occupation numbers of a two-level system and of a one-dimensional model for the hydrogen atom.Comment: less typo

Nuclear Corrections to Hyperfine Structure in Light Hydrogenic Atoms

Hyperfine intervals in light hydrogenic atoms and ions are among the most accurately measured quantities in physics. The theory of QED corrections has recently advanced to the point that uncalculated terms for hydrogenic atoms and ions are probably smaller than 0.1 parts per million (ppm), and the experiments are even more accurate. The difference of the experiments and QED theory is interpreted as the effect on the hyperfine interaction of the (finite) nuclear charge and magnetization distributions, and this difference varies from tens to hundreds of ppm. We have calculated the dominant component of the 1s hyperfine interval for deuterium, tritium and singly ionized helium, using modern second-generation potentials to compute the nuclear component of the hyperfine splitting for the deuteron and the trinucleon systems. The calculated nuclear corrections are within 3% of the experimental values for deuterium and tritium, but are about 20% discrepant for singly ionized helium. The nuclear corrections for the trinucleon systems can be qualitatively understood by invoking SU(4) symmetry.Comment: 26 pages, 1 figure, latex - submitted to Physical Review

Calculating the Rest Tension for a Polymer of String Bits

We explore the application of approximation schemes from many body physics, including the Hartree-Fock method and random phase approximation (RPA), to the problem of analyzing the low energy excitations of a polymer chain made up of bosonic string bits. We accordingly obtain an expression for the rest tension $T_0$ of the bosonic relativistic string in terms of the parameters characterizing the microscopic string bit dynamics. We first derive an exact connection between the string tension and a certain correlation function of the many-body string bit system. This connection is made for an arbitrary interaction potential between string bits and relies on an exact dipole sum rule. We then review an earlier calculation by Goldstone of the low energy excitations of a polymer chain using RPA. We assess the accuracy of the RPA by calculating the first order corrections. For this purpose we specialize to the unique scale invariant potential, namely an attractive delta function potential in two (transverse) dimensions. We find that the corrections are large, and discuss a method for summing the large terms. The corrections to this improved RPA are roughly 15\%.Comment: 44 pages, phyzzx, psfig required, Univ. of Florida preprint, UFIFT-HEP-94

Enumerative aspects of the Gross-Siebert program

We present enumerative aspects of the Gross-Siebert program in this introductory survey. After sketching the program's main themes and goals, we review the basic definitions and results of logarithmic and tropical geometry. We give examples and a proof for counting algebraic curves via tropical curves. To illustrate an application of tropical geometry and the Gross-Siebert program to mirror symmetry, we discuss the mirror symmetry of the projective plane.Comment: A version of these notes will appear as a chapter in an upcoming Fields Institute volume. 81 page

An Archaeological Survey for Asylum Creek and No Name Creek Channel Rectification Project, Bexar County, Texas

During August of 1992, staff archaeologists from the Center for Archaeological Research (CAR) at the University of Texas at San Antonio (UTSA) conducted surface survey, mapping, and subsurface testing adjacent to Asylum and No-Name Creeks under contract with the San Antonio River Authority in conjunction with a channel rectification project. Particular attention was given to locating cultural materials associated with the nearby San Juan Acequia. No significant cultural resources were located at either location

Viscous coalescence of droplets: a Lattice Boltzmann study

The coalescence of two resting liquid droplets in a saturated vapor phase is investigated by Lattice Boltzmann simulations in two and three dimensions. We find that, in the viscous regime, the bridge radius obeys a t^{1/2}-scaling law in time with the characteristic time scale given by the viscous time. Our results differ significantly from the predictions of existing analytical theories of viscous coalescence as well as from experimental observations. While the underlying reason for these deviations is presently unknown, a simple scaling argument is given that describes our results well.Comment: 12 pages, 10 figures; as published in Phys. Fluid

Computing in String Field Theory Using the Moyal Star Product

Using the Moyal star product, we define open bosonic string field theory carefully, with a cutoff, for any number of string oscillators and any oscillator frequencies. Through detailed computations, such as Neumann coefficients for all string vertices, we show that the Moyal star product is all that is needed to give a precise definition of string field theory. The formulation of the theory as well as the computation techniques are considerably simpler in the Moyal formulation. After identifying a monoid algebra as a fundamental mathematical structure in string field theory, we use it as a tool to compute with ease the field configurations for wedge, sliver, and generalized projectors, as well as all the string interaction vertices for perturbative as well as monoid-type nonperturbative states. Finally, in the context of VSFT we analyze the small fluctuations around any D-brane vacuum. We show quite generally that to obtain nontrivial mass and coupling, as well as a closed strings, there must be an associativity anomaly. We identify the detailed source of the anomaly, but leave its study for future work.Comment: 77 pages, LaTeX. v3: corrections of signs or factors (for a list of corrections see beginning of source file