Type IIA Orientifold Limit of M-Theory on Compact Joyce 8-Manifold of Spin(7)-Holonomy

We show that M-theory compactified on a compact Joyce 8-manifold of $Spin(7)$-holonomy, which yields an effective theory in $D = 3$ with $\N$ = 1 supersymmetry, admits at some special points in it moduli space a description in terms of type IIA theory on an orientifold of compact Joyce 7-manifold of $G_2$-holonomy. We find the evidence in favour of this duality by computing the massless spectra on both M-thory side and type IIA side. For the latter, we compute the massless spectra by going to the orbifold limit of the Joyce 7-manifold.Comment: 26 pages, 2 eps figures, Latex file, two references and one footnote added, corrected some typo

Measuring systemic risk

We present a simple model of systemic risk and show how each financial institution’s contribution to systemic risk can be measured and priced. An institution’s contribution, denoted systemic expected shortfall (SES), is its propensity to be undercapitalized when the system as a whole is undercapitalized, which increases in its leverage, volatility, correlation, and tail-dependence. Institutions internalize their externality if they are “taxed” based on their SES. Through several examples, we demonstrate empirically the ability of components of SES to predict emerging systemic risk during the nancial crisis of 2007-2009.Systemic risk ; Risk

G(2) quivers

We present, in explicit matrix representation and a modernity befitting the community, the classification of the finite discrete subgroups of G2 and compute the McKay quivers arising therefrom. Of physical interest are the classes of Script N = 1 gauge theories descending from M-theory and of mathematical interest are possible steps toward a systematic study of crepant resolutions to smooth G2 manifolds as well as generalised McKay Correspondences. This writing is a companion monograph to hep-th/9811183 and hep-th/9905212, wherein the analogues for Calabi-Yau three- and four-folds were considered