Gauge Fields and D-branes

We prove that self-dual gauge fields in type I superstring theory are equivalent to configurations of Dirichlet 5-branes, by showing that the world-sheet theory of a Dirichlet 1-brane moving in a background of 5-branes includes an ``ADHM sigma model.'' This provides an explicit construction of the equivalent self-dual gauge field. We also discuss type II.Comment: harvmac, 9p

Probing F-theory With Branes

Last week, A. Sen found an explicit type I string compactification dual to the eight-dimensional F-theory construction with SO(8)^4 nonabelian gauge symmetry. He found that the perturbations around the enhanced symmetry point were described by the mathematics of the solution of N=2, d=4 SU(2) gauge theory with four flavors, and argued more generally that global symmetry enhancement in CN=2, d=4 gauge theories corresponded to gauge symmetry enhancement in F-theory. We show that these N=2, d=4 gauge theories have a physical interpretation in the theory. They are the world-volume theories of 3-branes parallel to the 7-branes. They can be used to probe the structure of the exact quantum F-theory solutions. On the Higgs branch of the moduli space, the objects are equivalent to finite size instantons in the 7-brane gauge theory.Comment: harvmac, 7 p

Chiral Rings and Anomalies in Supersymmetric Gauge Theory

Motivated by recent work of Dijkgraaf and Vafa, we study anomalies and the chiral ring structure in a supersymmetric U(N) gauge theory with an adjoint chiral superfield and an arbitrary superpotential. A certain generalization of the Konishi anomaly leads to an equation which is identical to the loop equation of a bosonic matrix model. This allows us to solve for the expectation values of the chiral operators as functions of a finite number of ``integration constants.'' From this, we can derive the Dijkgraaf-Vafa relation of the effective superpotential to a matrix model. Some of our results are applicable to more general theories. For example, we determine the classical relations and quantum deformations of the chiral ring of $\N=1$ super Yang-Mills theory with SU(N) gauge group, showing, as one consequence, that all supersymmetric vacua of this theory have a nonzero chiral condensate.Comment: 67 pages, minor change

Dual Catalysis in Enantioselective Oxidopyrylium-Based [5+2] Cycloadditions

A new method is reported for effecting catalytic enantioselective intramolecular [5+2] cycloadditions based on oxidopyrylium intermediates. The dual catalyst system consists of a chiral primary aminothiourea and a second achiral thiourea. Experimental evidence points to a new type of cooperative catalysis with each species being necessary to generate a reactive pyrylium ion pair which undergoes subsequent cycloaddition with high enantioselectivity.Chemistry and Chemical Biolog

New meta-Terphenyl-Derived Primary Amines in Asymmetric Catalysis

In this dissertation, two distinct asymmetric reaction types are described: [5 + 2] pyrylium cycloadditions and aldehyde α-functionalizations. Both reactions are mediated by simple, organic primary amine catalysts bearing bulky meta-terphenyl moieties. The main text of this thesis is divided into five chapters outlining the relevant background and the original research. Chapter 1 provides a thorough historical overview of [5 + 2] oxidopyrylium cycloadditions and related asymmetric [3 + 2] cycloadditions. Early discoveries of intermolecular and intramolecular processes, asymmetric precedents, and pertinent frontier molecular orbital considerations are examined. The application of these transformations to the synthesis of natural products and bioactive compounds is also discussed. In Chapter 2, a new method for effecting catalytic enantioselective intramolecular [5 + 2] cycloadditions based on oxidopyrylium intermediates is presented. The development and employment of a dual catalyst system—consisting of a chiral m-terphenyl-containing primary aminothiourea and a second achiral thiourea—are described. Experimental evidence points to a new type of cooperative catalysis with each species being necessary to generate a reactive pyrylium ion pair that undergoes subsequent cycloaddition with high enantioselectivity. Chapter 3 details the successful expansion of the enantioselective [5 + 2] methodology to intermolecular reactions. Highly enantioselective intermolecular [5 + 2] cycloadditions of pyrylium ion intermediates with electron-rich alkenes are promoted by the same dual catalyst system as in Chapter 2. The observed enantioselectivity is highly dependent on the substitution pattern of the 5π component, and the basis for this effect is analyzed in detail using experimental and computational evidence. The resultant 8-oxabicyclo[3.2.1]octane derivatives possess a scaffold common in natural products and medicinally active compounds and are also versatile chiral building blocks for further manipulations. Several stereoselective complexity-generating transformations of the 8-oxabicyclooctane products are described. In Chapter 4, we transition into a literature survey of catalytic asymmetric α-functionalizations of α-branched aldehydes. First, the challenges associated with the efficient functionalization of such substrates, relative to their unbranched counterparts, are detailed. This introduction is followed by a comprehensive overview of catalytic, enantioselective α-heterofunctionalizations: aminations, oxygenations, sulfenylations, and fluorinations. Advantages and drawbacks to previously described methods are analyzed in detail. Chapter 5 recounts our own contributions to this area. A new chiral m-terphenyl-containing primary amine catalyst for the asymmetric α-hydroxylation and α-fluorination of α-branched aldehydes is reported. The products of the title transformations are isolated in high yields and exceptional enantioselectivities within short reaction times. Both processes can be performed at high concentrations and on gram scale. The remarkable similarity between the procedures, combined with computational evidence, implies a possible general catalytic mechanism for α-functionalizations. Promising initial results for α-amination and α-chlorination support this hypothesis.Chemistry and Chemical Biolog

Orbifold Resolution by D-Branes

We study topological properties of the D-brane resolution of three-dimensional orbifold singularities, C^3/Gamma, for finite abelian groups Gamma. The D-brane vacuum moduli space is shown to fill out the background spacetime with Fayet--Iliopoulos parameters controlling the size of the blow-ups. This D-brane vacuum moduli space can be classically described by a gauged linear sigma model, which is shown to be non-generic in a manner that projects out non-geometric regions in its phase diagram, as anticipated from a number of perspectives.Comment: 26 pages, 2 figures (TeX, harvmac big, epsf

Small Instantons, del Pezzo Surfaces and Type I' theory

Small instantons of exceptional groups arise geometrically by a collapsing del Pezzo surface in a CY. We use this to explain the physics of a 4-brane probe in Type I' compactification to 9 dimensions.Comment: 21 pages, minor change

D-branes and Discrete Torsion II

We derive D-brane gauge theories for C^3/Z_n x Z_n orbifolds with discrete torsion and study the moduli space of a D-brane at a point. We show that, as suggested in previous work, closed string moduli do not fully resolve the singularity, but the resulting space -- containing n-1 conifold singularities -- is somewhat surprising. Fractional branes also have unusual properties. We also define an index which is the CFT analog of the intersection form in geometric compactification, and use this to show that the elementary D6-brane wrapped about T^6/Z_n x Z_n must have U(n) world-volume gauge symmetry.Comment: harvmac, 25 p

Probing F-theory With Multiple Branes

We study multiple 3-branes on an F theory orientifold. The world-volume theory of the 3-branes is d=4, N=2 Sp(2k) gauge theory with an antisymmetric tensor and four flavors of matter in the fundamental. The solution of this gauge theory is found for vanishing bare mass of the antisymmetric tensor matter, and massive fundamental matter. The integrable system underlying this theory is constructed.Comment: 9 pages, harvma

D-branes and Short Distances in String Theory

We study the behavior of D-branes at distances far shorter than the string length scale~$l_s$. We argue that short-distance phenomena are described by the IR behavior of the D-brane world-volume quantum theory. This description is valid until the brane motion becomes relativistic. At weak string coupling \gs this corresponds to momenta and energies far above string scale. We use 0-brane quantum mechanics to study 0-brane collisions and find structure at length scales corresponding to the eleven-dimensional Planck length (\lp11 \sim \gs^{1/3} l_s) and to the radius of the eleventh dimension in M-theory (\R11 \sim \gs l_s). We use 0-branes to probe non-trivial geometries and topologies at sub-stringy scales. We study the 0-brane 4-brane system, calculating the 0-brane moduli space metric, and find the bound state at threshold, which has characteristic size \lp11. We examine the blowup of an orbifold and are able to resolve the resulting $S^2$ down to size \lp11. A 0-brane with momentum approaching $1/\R11$ is able to explore a larger configuration space in which the blowup is embedded. Analogous phenomena occur for small instantons. We finally turn to 1-branes and calculate the size of a bound state to be \sim \gs^{1/2} l_s, the 1-brane tension scale.Comment: 50 pages, harvmac, 3 epsf figures. References added, minor changes in tex