Noncommutative GUT inspired theories and the UV finiteness of the fermionic four point functions

We show at one-loop and first order in the noncommutativity parameters that in any noncommutative GUT inspired theory the total contribution to the fermionic four point functions coming only from the interaction between fermions and gauge bosons, though not UV finite by power counting, is UV finite at the end of the day. We also show that this is at odds with the general case for noncommutative gauge theories --chiral or otherwise-- defined by means of Seiberg-Witten maps that are the same --barring the gauge group representation-- for left-handed spinors as for right-handed spinors. We believe that the results presented in this paper tilt the scales to the side of noncommutative GUTS and noncommutative GUT inspired versions of the Standard Model.Comment: 11 pages, 3 figures. Version 2: references fixed and completed. Version 3: Comments adde

The Seiberg-Witten map and supersymmetry

The lack of any local solution to the first-order-in-h omegamn Seiberg-Witten (SW) map equations for U(1) vector superfields compels us to obtain the most general solution to those equations that is a quadratic polynomial in the ordinary vector superfield, v, its chiral and antichiral projections and the susy covariant derivatives of them all. Furnished with this solution, which is local in the susy Landau gauge, we construct an ordinary dual of noncommutative U(1) SYM in terms of ordinary fields which carry a linear representation of the N=1 susy algebra. By using the standard SW map for the N=1 U(1) gauge supermultiplet we define an ordinary U(1) gauge theory which is dual to noncommutative U(1) SYM in the WZ gauge. We show that the ordinary dual so obtained is supersymmetric, for, as we prove as we go along, the ordinary gauge and fermion fields that we use to define it carry a nonlinear representation of the N=1 susy algebra. We finally show that the two ordinary duals of noncommutative U(1) SYM introduced above are actually the same N=1 susy gauge theory. We also show in this paper that the standard SW map is never the theta theta--bar component of a local superfield in v and check that, at least at a given approximation, a suitable field redefinition of that map makes the noncommutative and ordinary --in a Bmn field-- susy U(1) DBI actions equivalent.Comment: 28 pages. No figure

Dynamic heterogeneity in the glass-like monoclinic phases of some halogen methane compounds

In this work we study the heterogeneity of the dynamics on the low-temperature monoclinic phases of the simple molecular glassy systems CBrnCl4−nCBrnCl4−n, n = 0, 1, 2. In these systems the disorder comes exclusively from reorientational jumps mainly around the C3 molecular axes. The different time scales are determined by means of the analysis of the spin-lattice relaxation time obtained through Nuclear Quadrupole Resonance (NQR) technique. Results are compared with those obtained from dielectric spectroscopy, from which two α- and β-relaxation times appear. NQR results enable us to ascribe with no doubt that the existence of two relaxations is due to dynamical heterogeneities which are the consequence of the different molecular surroundings of the molecules in the asymmetric unit cell of systems here studied.Fil: Zuriaga, Mariano Jose. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; ArgentinaFil: Perez, S. C.. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; ArgentinaFil: Pardo, L. C.. Universidad Politecnica de Catalunya; EspañaFil: Tamarit, J. L.. Universidad Politecnica de Catalunya; Españ

Influence of Refractory Periods in the Hopfield model

We study both analytically and numerically the effects of including refractory periods in the Hopfield model for associative memory. These periods are introduced in the dynamics of the network as thresholds that depend on the state of the neuron at the previous time. Both the retrieval properties and the dynamical behaviour are analyzed.Comment: Revtex, 7 pages, 7 figure

The U(1)A anomaly in noncommutative SU(N) theories

We work out the one-loop $U(1)_A$ anomaly for noncommutative SU(N) gauge theories up to second order in the noncommutative parameter $\theta^{\mu\nu}$. We set $\theta^{0i}=0$ and conclude that there is no breaking of the classical $U(1)_A$ symmetry of the theory coming from the contributions that are either linear or quadratic in $\theta^{\mu\nu}$. Of course, the ordinary anomalous contributions will be still with us. We also show that the one-loop conservation of the nonsinglet currents holds at least up to second order in $\theta^{\mu\nu}$. We adapt our results to noncommutative gauge theories with SO(N) and U(1) gauge groups.Comment: 50 pages, 5 figures in eps files. Some comments and references adde