D-branes in Massive IIA and Solitons in Chern-Simons Theory

We investigate D2-branes and D4-branes parallel to D8-branes. The low energy world volume theory on the branes is non-supersymmetric Chern-Simons theory. We identify the fundamental strings as the anyons of the 2+1 Chern-Simons theory and the D0-branes as solitons. The Chern-Simons theory with a boundary is modeled using NS 5-branes with ending D6-branes. The brane set-up provides for a graphical description of anomaly inflow. We also model the 4+1 Chern-Simons theory using branes and conjecture that D4-branes with a boundary describes a supersymmetric version of Kaplan's theory of chiral fermions.Comment: 22 pages, 4 figures, harvmac, epsf, references added, sec 4.2 adde

Type IIA Superstrings, Chiral Symmetry, and N=1 4D Gauge Theory Dualities

We study N=1 four dimensional gauge theories as the world volume theory of D4-branes between NS 5-branes. We find constructions for a number of known field theory dualities involving $SU(N_c)\times SU(N_c')$ groups, coupled by matter fields F in the $(N_c, \bar N_c)$ representation, in terms of branes of type IIA string theory. The dual gauge group follows from simply reversing the ordering of the NS 5-branes and the D6-branes while conserving magnetic charge on the world volume of the branes. We interpret many field theory phenomena such as deformation of the superpotential W = \Tr (F\tilde F)^{k+1} in terms of the position of branes. By looking to D-branes for guidance, we find new N=1 dualities involving arbitrary numbers of gauge groups. We propose a mechanism for enhanced chiral symmetry in the brane construction which, we conjecture, is associated with tensionless threebranes in six dimensions.Comment: 32 pages, 9 figures, uses harvmac, tables, and eps

Exact Solutions of Exceptional Gauge Theories from Toric Geometry

We derive four dimensional gauge theories with exceptional groups $F_4$, $E_8$, $E_7$, and $E_7$ with matter, by starting from the duality between the heterotic string on $K3$ and F-theory on a elliptically fibered Calabi-Yau 3-fold. This configuration is compactified to four dimensions on a torus, and by employing toric geometry, we compute the type IIB mirrors of the Calabi-Yaus of the type IIA string theory. We identify the Seiberg-Witten curves describing the gauge theories as ALE spaces fibered over a $P^1$ base.Comment: 18 pages, 5 figures, uses harvmac and eps

Two Dimensional Mirror Symmetry From M-theory

We construct two dimensional gauge theories with $N= (4,4)$ supersymmetry from branes of type IIA string theory. Quantum effects in the two dimensional gauge theory are analyzed by embedding the IIA brane construction into M-theory. We find that the Coulomb branch of one theory and the Higgs branch of a mirror theory become equivalent at strong coupling. A relationship to the decoupling limit of the type IIA and IIB 5-branes in Matrix theory is shown. T-duality between the ALE metric and the wormhole metric of Callan, Harvey, and Strominger is discussed from a brane perspective and some puzzles regarding string duality resolved. We comment on the existence of a quantum Higgs branch in two dimensional theories. Branes prove to be useful tools in analyzing singular conformal field theories.Comment: 21 pages, 3 figures, uses harvmac and eps

Patterns of Duality in N=1 SUSY Gauge Theories

We study the patterns in the duality of a wide class of N=1 supersymmetric gauge theories in four dimensions. We present many new generalizations of the classic duality models of Kutasov and Schwimmer, which have themselves been generalized numerous times in works of Intriligator, Leigh and the present authors. All of these models contain one or two fields in a two-index tensor representation, along with fields in the defining representation. The superpotential for the two-index tensor(s) resembles A_k or D_k singularity forms, generalized from numbers to matrices. Looking at the ensemble of these models, classifying them by superpotential, gauge group, and ``level'' -- for terminology we appeal to the architecture of a typical European-style theatre -- we identify emerging patterns and note numerous interesting puzzles.Comment: 34 pages, 4 figures, uses harvmac and table

The Age Difference between the Globular Cluster Sub-populations in NGC 4472

The age difference between the two main globular cluster sub-populations in the Virgo giant elliptical galaxy, NGC 4472 (M 49), has been determined using HST WFPC2 images in the F555W and F814W filters. Accurate photometry has been obtained for several hundred globular clusters in each of the two main sub-populations, down to more than one magnitude below the turn-over of their luminosity functions. This allows precise determinations of both the mean colors and the turn-over magnitudes of the two main sub-populations. By comparing the data with various population synthesis models, the age-metallicity pairs that fit both the observed colors and magnitudes have been identified. The metal-poor and the metal-rich globular clusters are found to be coeval within the errors ($\sim 3$ Gyr). If one accepts the validity of our assumptions, these errors are dominated by model uncertainties. A systematic error of up to 4 Gyr could affect this result if the blue and the red clusters have significantly different mass distributions. However, that one sub-population is half as old as the other is excluded at the 99% confidence level. The different globular cluster populations are assumed to trace the galaxy's major star-formation episodes. Consequently, the vast majority of globular clusters, and by implication the majority of stars, in NGC 4472 formed at high redshifts but by two distinct mechanisms or in two episodes.Comment: 32 pages, including 12 postscript figures, accepted for publication in the Astronomical Journal, December 1999 issu