On the Construction and the Structure of Off-Shell Supermultiplet Quotients

Recent efforts to classify representations of supersymmetry with no central charge have focused on supermultiplets that are aptly depicted by Adinkras, wherein every supersymmetry generator transforms each component field into precisely one other component field or its derivative. Herein, we study gauge-quotients of direct sums of Adinkras by a supersymmetric image of another Adinkra and thus solve a puzzle from Ref.[2]: The so-defined supermultiplets do not produce Adinkras but more general types of supermultiplets, each depicted as a connected network of Adinkras. Iterating this gauge-quotient construction then yields an indefinite sequence of ever larger supermultiplets, reminiscent of Weyl's construction that is known to produce all finite-dimensional unitary representations in Lie algebras.Comment: 20 pages, revised to clarify the problem addressed and solve

On Graph-Theoretic Identifications of Adinkras, Supersymmetry Representations and Superfields

In this paper we discuss off-shell representations of N-extended supersymmetry in one dimension, ie, N-extended supersymmetric quantum mechanics, and following earlier work on the subject codify them in terms of certain graphs, called Adinkras. This framework provides a method of generating all Adinkras with the same topology, and so also all the corresponding irreducible supersymmetric multiplets. We develop some graph theoretic techniques to understand these diagrams in terms of a relatively small amount of information, namely, at what heights various vertices of the graph should be "hung". We then show how Adinkras that are the graphs of N-dimensional cubes can be obtained as the Adinkra for superfields satisfying constraints that involve superderivatives. This dramatically widens the range of supermultiplets that can be described using the superspace formalism and organizes them. Other topologies for Adinkras are possible, and we show that it is reasonable that these are also the result of constraining superfields using superderivatives. The family of Adinkras with an N-cubical topology, and so also the sequence of corresponding irreducible supersymmetric multiplets, are arranged in a cyclical sequence called the main sequence. We produce the N=1 and N=2 main sequences in detail, and indicate some aspects of the situation for higher N.Comment: LaTeX, 58 pages, 52 illustrations in color; minor typos correcte

Asymmetric Non-Abelian Orbifolds and Model Building

The rules for the free fermionic string model construction are extended to include general non-abelian orbifold constructions that go beyond the real fermionic approach. This generalization is also applied to the asymmetric orbifold rules recently introduced. These non-abelian orbifold rules are quite easy to use. Examples are given to illustrate their applications.Comment: 30 pages, Revtex 3.

Fake R^4's, Einstein Spaces and Seiberg-Witten Monopole Equations

We discuss the possible relevance of some recent mathematical results and techniques on four-manifolds to physics. We first suggest that the existence of uncountably many R^4's with non-equivalent smooth structures, a mathematical phenomenon unique to four dimensions, may be responsible for the observed four-dimensionality of spacetime. We then point out the remarkable fact that self-dual gauge fields and Weyl spinors can live on a manifold of Euclidean signature without affecting the metric. As a specific example, we consider solutions of the Seiberg-Witten Monopole Equations in which the U(1) fields are covariantly constant, the monopole Weyl spinor has only a single constant component, and the 4-manifold M_4 is a product of two Riemann surfaces Sigma_{p_1} and Sigma_{p_2}. There are p_{1}-1(p_{2}-1) magnetic(electric) vortices on \Sigma_{p_1}(\Sigma_{p_2}), with p_1 + p_2 \geq 2 (p_1=p_2= 1 being excluded). When the two genuses are equal, the electromagnetic fields are self-dual and one obtains the Einstein space \Sigma_p x \Sigma_p, the monopole condensate serving as the cosmological constant.Comment: 9 pages, Talk at the Second Gursey Memorial Conference, June 2000, Istanbu

Ultrastable CO2 Laser Trapping of Lithium Fermions

We demonstrate an ultrastable CO2 laser trap that provides tight confinement of neutral atoms with negligible optical scattering and minimal laser-noise- induced heating. Using this method, fermionic 6Li atoms are stored in a 0.4 mK deep well with a 1/e trap lifetime of 300 sec, consistent with a background pressure of 10^(-11) Torr. To our knowledge, this is the longest storage time ever achieved with an all-optical trap, comparable to the best reported magnetic traps.Comment: 4 pages using REVTeX, 1 eps figur

The curvature of semidirect product groups associated with two-component Hunter-Saxton systems

In this paper, we study two-component versions of the periodic Hunter-Saxton equation and its $\mu$-variant. Considering both equations as a geodesic flow on the semidirect product of the circle diffeomorphism group \Diff(\S) with a space of scalar functions on $\S$ we show that both equations are locally well-posed. The main result of the paper is that the sectional curvature associated with the 2HS is constant and positive and that 2$\mu$HS allows for a large subspace of positive sectional curvature. The issues of this paper are related to some of the results for 2CH and 2DP presented in [J. Escher, M. Kohlmann, and J. Lenells, J. Geom. Phys. 61 (2011), 436-452].Comment: 19 page

Building a Better Racetrack

We find IIb compactifications on Calabi-Yau orientifolds in which all Kahler moduli are stabilized, along lines suggested by Kachru, Kallosh, Linde and Trivedi.Comment: 47 pages, 1 figure, harvmac (v2: added references, minor comments, v3: improved discussion of metastability and explicit flux vacua

KO-Homology and Type I String Theory

We study the classification of D-branes and Ramond-Ramond fields in Type I string theory by developing a geometric description of KO-homology. We define an analytic version of KO-homology using KK-theory of real C*-algebras, and construct explicitly the isomorphism between geometric and analytic KO-homology. The construction involves recasting the Cl(n)-index theorem and a certain geometric invariant into a homological framework which is used, along with a definition of the real Chern character in KO-homology, to derive cohomological index formulas. We show that this invariant also naturally assigns torsion charges to non-BPS states in Type I string theory, in the construction of classes of D-branes in terms of topological KO-cycles. The formalism naturally captures the coupling of Ramond-Ramond fields to background D-branes which cancel global anomalies in the string theory path integral. We show that this is related to a physical interpretation of bivariant KK-theory in terms of decay processes on spacetime-filling branes. We also provide a construction of the holonomies of Ramond-Ramond fields in Type II string theory in terms of topological K-chains.Comment: 40 pages; v4: Clarifying comments added, more detailed proof of main isomorphism theorem given; Final version to be published in Reviews in Mathematical Physic

Geometric K-Homology of Flat D-Branes

We use the Baum-Douglas construction of K-homology to explicitly describe various aspects of D-branes in Type II superstring theory in the absence of background supergravity form fields. We rigorously derive various stability criteria for states of D-branes and show how standard bound state constructions are naturally realized directly in terms of topological K-cycles. We formulate the mechanism of flux stabilization in terms of the K-homology of non-trivial fibre bundles. Along the way we derive a number of new mathematical results in topological K-homology of independent interest.Comment: 45 pages; v2: References added; v3: Some substantial revision and corrections, main results unchanged but presentation improved, references added; to be published in Communications in Mathematical Physic