Non-commutativity and Supersymmetry

We study the extent to which the gauge symmetry of abelian Yang-Mills can be deformed under two conditions: first, that the deformation depend on a two-form scale. Second, that the deformation preserve supersymmetry. We show that (up to a single parameter) the only allowed deformation is the one determined by the star product. We then consider the supersymmetry algebra satisfied by NCYM expressed in commutative variables. The algebra is peculiar since the supercharges are not gauge-invariant. However, the action, expressed in commutative variables, appears to be quadratic in fermions to all orders in theta.Comment: 21 pages, LaTeX; a reference adde

Topological quantization and degeneracy in Josephson-junction arrays

We consider the conductivity quantization in two-dimensional arrays of mesoscopic Josephson junctions, and examine the associated degeneracy in various regimes of the system. The filling factor of the system may be controlled by the gate voltage as well as the magnetic field, and its appropriate values for quantization is obtained by employing the Jain hierarchy scheme both in the charge description and in the vortex description. The duality between the two descriptions then suggests the possibility that the system undergoes a change in degeneracy while the quantized conductivity remains fixed.Comment: To appear in Phys. Rev.

Interacting Open Wilson Lines in Noncommutative Field Theories

In noncommutative field theories, it was known that one-loop effective action describes propagation of non-interacting open Wilson lines, obeying the flying dipole's relation. We show that two-loop effective action describes cubic interaction among `closed string' states created by open Wilson lines. Taking d-dimensional noncommutative [\Phi^3] theory as the simplest setup, we compute nonplanar contribution at low-energy and large noncommutativity limit. We find that the contribution is expressible in a remarkably simple cubic interaction involving scalar open Wilson lines only and nothing else. We show that the interaction is purely geometrical and noncommutative in nature, depending only on sizes of each open Wilson line.Comment: v1: 27 pages, Latex, 7 .eps figures v2: minor wording change + reference adde

A cell cycle model for somitogenesis: mathematical formulation and numerical simulation

After many years of research, the mechanisms that generate a periodic pattern of repeated elements (somites) along the length of the embryonic body axis is still one of the major unresolved problems in developmental biology. Here we present a mathematical formulation of the cell cycle model for somitogenesis proposed in Development105 (1989), 119–130. Somite precursor cells in the node are asynchronous, and therefore, as a population, generate continuously pre-somite cells which enter the segmental plate. The model makes the hypothesis that there exists a time window within the cell cycle, making up one-seventh of the cycle, which gates the pre-somite cells so that they make somites discretely, seven per cycle. We show that the model can indeed account for the spatiotemporal patterning of somite formation during normal development as well as the periodic abnormalities produced by heat shock treatment. We also relate the model to recent molecular data on the process of somite formation

Cosmokinetics: A joint analysis of Standard Candles, Rulers and Cosmic Clocks

We study the accelerated expansion of the universe by using the kinematic approach. In this context, we parameterize the deceleration parameter, q(z), in a model independent way. Assuming three simple parameterizations we reconstruct q(z). We do the joint analysis with combination of latest cosmological data consisting of standard candles (Supernovae Union2 sample), standard ruler (CMB/BAO), cosmic clocks (age of passively evolving galaxies) and Hubble (H(z)) data. Our results support the accelerated expansion of the universe.Comment: PDFLatex, 15 pages, 12 pdf figures, revised version to appear in JCA

Crossover between ionic/covalent and pure ionic bonding in magnesium oxyde clusters

An empirical potential with fluctuating charges is proposed for modelling (MgO)_n clusters in both the molecular (small n) and bulk (n->infty) regimes. Vectorial polarization forces are explicitely taken into account in the self-consistent determination of the charges. Our model predicts cuboid cluster structures, in agreement with previous experimental and theoretical results. The effective charge transferred between magnesium and oxygen smoothly increases from 1 to 2, with an estimated crossover size above 300 MgO molecules

Anomaly-matching and Higgs-less effective theories

We reconsider the low-energy effective theory for Higgs-less electroweak symmetry breaking: we study the anomaly-matching in the situation where all Goldstone fields disappear from the spectrum as a result of the Higgs mechanism. We find that the global SU(2)_L x SU(2)_R x U(1)_{B-L} symmetry of the underlying theory, which is spontaneously broken to SU(2)_{L+R} x U(1)_{B-L} has to be anomaly-free. For the sake of generality, we include the possibility of light spin-1/2 bound states resulting from the dynamics of the strongly-interacting symmetry-breaking sector, in addition to the Goldstone bosons. Such composite fermions may have non-standard couplings at the leading order, and an arbitrary total B-L charge. In order to perform the anomaly-matching in that case, we generalize the construction of the Wess-Zumino effective lagrangian. Composite fermions beyond the three known generations are theoretically allowed, and there are no restrictions from the anomaly-matching on their couplings nor on their U(1)_{B-L} charge. Absence of global anomalies for the composite sector as a whole does not preclude anomalous triple gauge boson couplings arising from composite fermion triangular diagrams. On the other hand, the trace of B-L over elementary fermions must vanish if all Goldstone modes are to disappear from the spectrum.Comment: Keywords: Anomalies in Field and String Theories, Spontaneous Symmetry Breaking, Beyond the Standard Model, Chiral Lagrangians. 33 pages, 7 figure

Two-dimensional limit of exchange-correlation energy functional approximations in density functional theory

We investigate the behavior of three-dimensional (3D) exchange-correlation energy functional approximations of density functional theory in anisotropic systems with two-dimensional (2D) character. Using two simple models, quasi-2D electron gas and two-electron quantum dot, we show a {\it fundamental limitation} of the local density approximation (LDA), and its semi-local extensions, generalized gradient approximation (GGA) and meta-GGA (MGGA), the most widely used forms of which are worse than the LDA in the strong 2D limit. The origin of these shortcomings is in the inability of the local (LDA) and semi-local (GGA/MGGA) approximations to describe systems with 2D character in which the nature of the exchange-correlation hole is very nonlocal. Nonlocal functionals provide an alternative approach, and explicitly the average density approximation (ADA) is shown to be remarkably accurate for the quasi-2D electron gas system. Our study is not only relevant for understanding of the functionals but also practical applications to semiconductor quantum structures and materials such as graphite and metal surfaces. We also comment on the implication of our findings to the practical device simulations based on the (semi-)local density functional method.Comment: 21 pages including 9 figures, to be published in Phys. Rev.

Light quarks masses and condensates in QCD

We review some theoretical and phenomenological aspects of the scenario in which the spontaneous breaking of chiral symmetry is not triggered by a formation of a large condensate . Emphasis is put on the resulting pattern of light quark masses, on the constraints arising from QCD sum rules and on forthcoming experimental tests.Comment: 23 pages, 12 Postscript figures, LaTeX, uses svcon2e.sty, to be published in the Proceedings of the Workshop on Chiral Dynamics 1997, Mainz, Germany, Sept. 1-5, 199