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

Renormalisability of the matter determinants in noncommutative gauge theory in the enveloping-algebra formalism

We consider noncommutative gauge theory defined by means of Seiberg-Witten maps for an arbitrary semisimple gauge group. We compute the one-loop UV divergent matter contributions to the gauge field effective action to all orders in the noncommutative parameters $\theta$. We do this for Dirac fermions and complex scalars carrying arbitrary representations of the gauge group. We use path-integral methods in the framework of dimensional regularisation and consider arbitrary invertible Seiberg-Witten maps that are linear in the matter fields. Surprisingly, it turns out that the UV divergent parts of the matter contributions are proportional to the noncommutative Yang-Mills action where traces are taken over the representation of the matter fields; this result supports the need to include such traces in the classical action of the gauge sector of the noncommutative theory.Comment: 7 page

Renormalisability of noncommutative GUT inspired field theories with anomaly safe groups

We consider noncommutative GUT inspired field theories formulated within the enveloping-algebra formalism for anomaly safe compact simple gauge groups. Our theories have only gauge fields and fermions, and we compute the UV divergent part of the one-loop background-field effective action involving two fermionic fields at first order in the noncommutativity parameter theta. We show that, if the second-degree Casimir has the same value for all the irreps furnished by the fermionic multiplets of the model, then, that UV divergent part can be renormalised by carrying out multiplicative renormalisations of the coupling constant, theta and the fields, along with the inclusion of theta-dependent counterterms which vanish upon imposing the equations of motion. These theta-dependent counterterms have no physical effect since they vanish on-shell. This result along with the vanishing of the UV divergent part of the fermionic four-point functions leads to the unexpected conclusion that the one-loop matter sector of the background-field effective action of these theories is one-loop multiplicatively renormalisable on-shell. We also show that the background-field effective action of the gauge sector of the theories considered here receives no theta-dependent UV divergent contributions at one-loop. We thus conclude that these theories are on-shell one-loop multiplicatively renormalisable at first order in theta.Comment: 20 pages, 3 figure

Interplay of network structure and dynamics in functional organization of the visual cortex

The functional patterns of the visual cortex observed in some mammals such as cats, primates, and humans has allowed us to understand basic principles of organization in the structure of the cortex. However, the observation of different kinds of functional arrangement in other animals such as mice, rats, rabbits, and squirrels, called salt and pepper patterns, raise questions about which of these principles can be transferred to the understanding of visual processing in general. In order to gain insight into these basic principles, in this work we propose a simple model for the formation of spatiotemporal patterns in the visual cortex. The model is based on coupled phase oscillators that interact through an evolving complex network that is embedded in a two-dimensional Euclidean space. In this way we are able to explore the relation between network structure and functional organization. We find that the model allows for the emergence of clustered synchronized states that are spatially segregated as some orientation maps, and also synchronized states that are spatially interspersed, resembling salt and pepper organizational maps.Fil: Daza Caro, Yudy Carolina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; ArgentinaFil: Gleiser, Pablo Martin. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; ArgentinaFil: Tamarit, Francisco. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentin

Noncommutative N=1 super Yang-Mills, the Seiberg-Witten map and UV divergences

Classically, the dual under the Seiberg-Witten map of noncommutative U(N), {\cal N}=1 super Yang-Mills theory is a field theory with ordinary gauge symmetry whose fields carry, however, a \theta-deformed nonlinear realisation of the {\cal N}=1 supersymmetry algebra in four dimensions. For the latter theory we work out at one-loop and first order in the noncommutative parameter matrix \theta^{\mu\nu} the UV divergent part of its effective action in the background-field gauge, and, for N>=2, we show that for finite values of N the gauge sector fails to be renormalisable; however, in the large N limit the full theory is renormalisable, in keeping with the expectations raised by the quantum behaviour of the theory's noncommutative classical dual. We also obtain --for N>=3, the case with N=2 being trivial-- the UV divergent part of the effective action of the SU(N) noncommutative theory in the enveloping-algebra formalism that is obtained from the previous ordinary U(N) theory by removing the U(1) degrees of freedom. This noncommutative SU(N) theory is also renormalisable.Comment: 33 pages, 4 figures. Version 2: Unnecessary files removed. Version 3: New types of field redefinitions were considered, which make the large N U(N) and the SU(N) theories renormalisable. The conclusions for U(N) with finite N remain unchanged. Version 4: Corrected mistyped equations, minor revision

Monopoles, noncommutative gauge theories in the BPS limit and some simple gauge groups

For three conspicuous gauge groups, namely, SU(2), SU(3) and SO(5), and at first order in the noncommutative parameter matrix h\theta^{\mu\nu}, we construct smooth monopole --and, some two-monopole-- fields that solve the noncommutative Yang-Mills-Higgs equations in the BPS limit and that are formal power series in h\theta^{\mu\nu}. We show that there exist noncommutative BPS (multi-)monopole field configurations that are formal power series in h\theta^{\mu\nu} if, and only if, two a priori free parameters of the Seiberg-Witten map take very specific values. These parameters, that are not associated to field redefinitions nor to gauge transformations, have thus values that give rise to sharp physical effects.Comment: 30 pages, no figure

Decoupling heavy sparticles in Effective SUSY scenarios: Unification, Higgs masses and tachyon bounds

Using two-loop renormalization group equations implementing the decoupling of heavy scalars, Effective SUSY scenarios are studied in the limit in which there is a single low energy Higgs field. Gauge coupling unification is shown to hold with similar or better precision than in standard MSSM scenarios. b-tau unification is examined, and Higgs masses are computed using the effective potential, including two-loop contributions from scalars. A 125 GeV Higgs is compatible with stops/sbottoms at around 300 GeV with non-universal boundary conditions at the scale of the heavy sparticles if some of the trilinear couplings at this scale take values of the order of 1-2 TeV; if more constrained boundary conditions inspired by msugra or gauge mediation are set at a higher scale, heavier colored sparticles are required in general. Finally, since the decoupled RG flow for third-generation scalar masses departs very significantly from the MSSM DR-bar one, tachyon bounds for light scalars are revisited and shown to be relaxed by up to a TeV or more.Comment: 35 pages, 17 figures. v2: Updated some scans, allowing for changes in sign of some parameters, minor improvements. v3: Typos corrected in formulae in the appendices, added some clarifying remarks about flavor mixing being ignore