The Strength of Non-Perturbative Effects in Matrix Models and String Effective Lagrangians

We present a summary of the results of an explicit calculation of the strength of non-perturbative interactions in matrix models and string effective Lagrangians. These interactions are induced by single eigenvalue instantons in the $d=1$ bosonic matrix model. A well defined approximation scheme is used to obtain induced operators whose exact form we exhibit. We briefly discuss the possibility that similar instantons in a supersymmetric version of the theory may break supersymmetry dynamically.Comment: Latex document, 17 pages, preprint CERN-TH.7356/94, UPR-620

Supersymmetric Field Theory from Supermatrix Models

We show that the continuum limit of one-dimensional N=2 supersymmetric matrix models can be described by a two-dimensional interacting field theory of a massless boson and two chiral fermions. We interpret this field theory as a two-dimensional N=1 supersymmetric theory of two chiral superfields, in which one of the chiral superfields has a non-trivial vacuum expectation value.Comment: Latex document, 11 pages, preprint CERN-TH.7353/94, UPR-621

Twisted Sectors and Chern-Simons Terms in M-Theory Orbifolds

It is shown that the twisted sector spectrum, as well as the associated Chern-Simons interactions, can be determined on M-theory orbifold fixed planes that do not admit gravitational anomalies. This is demonstrated for the seven-planes arising within the context of an explicit $R^6 \times S^1/Z_2 \times T^4/Z_2$ orbifold, although the results are completely general. Local anomaly cancellation in this context is shown to require fractional anomaly data that can only arise from a twisted sector on the seven-planes, thus determining the twisted spectrum up to a small ambiguity. These results open the door to the construction of arbitrary M-theory orbifolds, including those containing fixed four-planes which are of phenomenological interest.Comment: 21 pages, LaTe

An M-Theory Perspective on Heterotic K3 Orbifold Compactifications

We analyze the structure of heterotic M-theory on K3 orbifolds by presenting a comprehensive sequence of M-theoretic models constructed on the basis of local anomaly cancellation. This is facilitated by extending the technology developed in our previous papers to allow one to determine "twisted" sector states in non-prime orbifolds. These methods should naturally generalize to four-dimensional models, which are of potential phenomenological interest.Comment: 58 pages, LaTe

A BPS Interpretation of Shape Invariance

We show that shape invariance appears when a quantum mechanical model is invariant under a centrally extended superalgebra endowed with an additional symmetry generator, which we dub the shift operator. The familiar mathematical and physical results of shape invariance then arise from the BPS structure associated with this shift operator. The shift operator also ensures that there is a one-to-one correspondence between the energy levels of such a model and the energies of the BPS-saturating states. These findings thus provide a more comprehensive algebraic setting for understanding shape invariance.Comment: 15 pages, 2 figures, LaTe

NetSci High: Bringing Agency to Diverse Teens Through the Science of Connected Systems

This paper follows NetSci High, a decade-long initiative to inspire teams of teenage researchers to develop, execute and disseminate original research in network science. The project introduced high school students to the computer-based analysis of networks, and instilled in the participants the habits of mind to deepen inquiry in connected systems and statistics, and to sustain interest in continuing to study and pursue careers in fields involving network analysis. Goals of NetSci High ranged from proximal learning outcomes (e.g., increasing high school student competencies in computing and improving student attitudes toward computing) to highly distal (e.g., preparing students for 21st century science), with an emphasis on doing real-world research into relevant and ambiguous problems through technologically-infused and highly collaborative projects and defending them to a clear (and sometimes potentially intimidating) audience. The cognitive goals of the project covered broad areas including analyzing, synthesizing, and visualizing quantitative data, and understanding modeling and network statistics. Attitudinal outcomes included improving attitudes toward the statistical study of networks, self-efficacy, and a sense of agency for continuing to pursue further involvement in college studies and careers

Effective Symmetries of the Minimal Supermultiplet of N = 8 Extended Worldline Supersymmetry

A minimal representation of the N = 8 extended worldline supersymmetry, known as the `ultra-multiplet', is closely related to a family of supermultiplets with the same, E(8) chromotopology. We catalogue their effective symmetries and find a Spin(4) x Z(2) subgroup common to them all, which explains the particular basis used in the original construction. We specify a constrained superfield representation of the supermultiplets in the ultra-multiplet family, and show that such a superfield representation in fact exists for all adinkraic supermultiplets. We also exhibit the correspondences between these supermultiplets, their Adinkras and the E(8) root lattice bases. Finally, we construct quadratic Lagrangians that provide the standard kinetic terms and afford a mixing of an even number of such supermultiplets controlled by a coupling to an external 2-form of fluxes.Comment: 13 Figure