Matrix Orientifolding and Models with Four or Eight Supercharges

The conditions under which matrix orientifolding and supersymmetry transformations commute are known to be stringent. Here we present the cases possessing four or eight supercharges upon ${\bf Z}_3$ orbifolding followed by matrix orientifolding. These cases descend from the matrix models with eight plus eight supercharges. There are fifty in total, which we enumerate.Comment: 17pages; references adde

Nonabelian Monopoles from Matrices: Seeds of the Spacetime Structure

We study the expectation value of (the product) of the one-particle projector (s) in the reduced matrix model and matrix quantum mechanics in general. This quantity is given by the nonabelian Berry phase: we discuss the relevance of this with regard to the spacetime structure. The case of the USp matrix model is examined from this respect. Generalizing our previous work, we carry out the complete computation of this quantity which takes into account both the nature of the degeneracy of the fermions and the presence of the space time points belonging to the antisymmetric representation. We find the singularities as those of the SU(2) Yang monopole connection as well as the pointlike singularities in 9+1 dimensions coming from its SU(8) generalization. The former type of singularities, which extend to four of the directions lying in the antisymmetric representations, may be regarded as seeds of our four dimensional spacetime structure and is not shared by the IIB matrix model. From a mathematical viewpoint, these connections can be generalizable to arbitrary odd space dimensions due to the nontrivial nature of the eigenbundle and the Clifford module structure.Comment: 29 pages, Latex, 1 epsf figur

Berry's Connection and USp(2k) Matrix Model

Berry's connection is computed in the USp(2k) matrix model. In T dualized quantum mechanics, the Berry phase exhibits a residual interaction taking place at a distance m_(f) from the orientifold surface via the integration of the fermions in the fundamental representation. This is interpreted as a coupling of the magnetic D2 with the electric D4 branes. We make a comment on the Berry phase associated with the 6D nonabelian gauge anomaly whose cancellation selects the number of flavours n_f=16.Comment: a few minor errors corrected, to appear in Phys. Lett.

126 GeV Higgs Boson Associated with D-term Triggered Dynamical Supersymmetry Breaking

Continuing with our previous work on D-term triggered dynamical supersymmetry breaking, we consider a system in which our generic N=1 action is minimally extended to include the pair of Higgs doublet superfields charged under the overall U(1) as well as mu and B mu terms. The gauge group is taken to be SU(3)_C times SU(2)_L times U(1)_Y times U(1). We point out, among other things, that the Higgs mass less than the Z-boson mass at tree level can be pushed up to be around 126 GeV by D-term contributions of the overall U(1). This is readily realized by taking a U(1) gauge coupling of O(1).Comment: 11 pages, 1 figure, A reference corrected, the argument of anomaly cancellation for an overall U(1) adde

Mass Sum Rule of the Effective Action on Vacua with Broken Rigid N=1 Supersymmetry

We present an extension of the mass sum rule that applies to renormalizable rigid supersymmetric field theories to the case of the N=1 supersymmetric effective action (the gauged non-linear sigma model) consisting of adjoint scalar superfields and vector superfields possessing a K"ahler potential, a set of gauge coupling functions (second prepotential derivatives) and a superpotential, which respectively set their energy scales. The mass sum rule derived is valid for any vacua, including the (metastable) one of broken supersymmetry with the condensates of D-term and/or F-term. We manage to extend these analyses to the cases where superfields in (anti-)fundamental representation are present. The supertrace is shown to vanish in those cases where underlying geometry is special K"ahler and theory under concern is anomaly free. Simple phenomenological application is given, providing an upper bound for gaugino masses. We discuss that the effects of the D and/or F condensates can be represented as a set of soft breaking terms with their strengths predicted by the scales.Comment: 18 pages, no figure

USp(2k) Matrix Model: Schwinger-Dyson Equations and Closed-Open String Interactions

We derive the Schwinger-Dyson/loop equations for the USp(2k) matrix model which close among the closed and open Wilson loop variables. These loop equations exhibit a complete set of the joining and splitting interactions required for the nonorientable Type I superstrings. The open loops realize the SO(2n_f) Chan-Paton factor and their linearized loop equations derive the mixed Dirichlet/Neumann boundary conditions.Comment: 22 pages, 13 figure

USp(2k) Matrix Model: F Theory Connection

We present a zero dimensional matrix model based on $USp(2k)$ with supermultiplets in symmetric, antisymmetric and fundamental representations. The four dimensional compactification of this model naturally captures the exact results of Sen \cite{Sen} in $F$ theory. Eight dynamical and eight kinematical supercharges are found, which is required for critical string interpretation. Classical vacuum has ten coordinates and is equipped with orbifold structure. We clarify the issue of spacetime dimensions which $F$ theory represented by this matrix model produces.Comment: 11 pages, Latex: interpretation as large T^{6}/Z^{2} IIB orientifold added, the final version to appear in Progress of Theoretical Physic