Confining the Electroweak Model to a Brane

We introduce a simple scenario where, by starting with a five-dimensional SU(3) gauge theory, we end up with several 4-D parallel branes with localized fermions and gauge fields. Similar to the split fermion scenario, the confinement of fermions is generated by the nontrivial topological solution of a SU(3) scalar field. The 4-D fermions are found to be chiral, and to have interesting properties coming from their 5-D group representation structure. The gauge fields, on the other hand, are localized by loop corrections taking place at the branes produced by the fermions. We show that these two confining mechanisms can be put together to reproduce the basic structure of the electroweak model for both leptons and quarks. A few important results are: Gauge and Higgs fields are unified at the 5-D level; and new fields are predicted: One left-handed neutrino with zero-hypercharge, and one massive vector field coupling together the new neutrino with other left-handed leptons. The hierarchy problem is also addressed.Comment: 9 pages, 8 figures; references added; version published in PR

Meron-cluster simulation of the quantum antiferromagnetic Heisenberg model in a magnetic field in one- and two-dimensions

Motivated by the numerical simulation of systems which display quantum phase transitions, we present a novel application of the meron-cluster algorithm to simulate the quantum antiferromagnetic Heisenberg model coupled to an external uniform magnetic field both in one and in two dimensions. In the infinite volume limit and at zero temperature we found numerical evidence that supports a quantum phase transition very close to the critical values $B_{c}=2$ and $B_{c}=4$ for the system in one and two dimensions, respectively. For the one dimensional system, we have compared the numerical data obtained with analytical predictions for the magnetization density as a function of the external field obtained by scaling-behaviour analysis and Bethe Ansatz techniques. Since there is no analytical solution for the two dimensional case, we have compared our results with the magnetization density obtained by scaling relations for small lattice sizes and with the approximated thermodynamical limit at zero temperature guessed by scaling relations. Moreover, we have compared the numerical data with other numerical simulations performed by using different algorithms in one and two dimensions, like the directed loop method. The numerical data obtained are in perfect agreement with all these previous results, which confirms that the meron-algorithm is reliable for quantum Monte Carlo simulations and applicable both in one and two dimensions. Finally, we have computed the integrated autocorrelation time to measure the efficiency of the meron algorithm in one dimension.Comment: 18 pages, 11 figure

The string swampland constraints require multi-field inflation

An important unsolved problem that affects practically all attempts to connect string theory to cosmology and phenomenology is how to distinguish effective field theories belonging to the string landscape from those that are not consistent with a quantum theory of gravity at high energies (the "string swampland"). It was recently proposed that potentials of the string landscape must satisfy at least two conditions, the "swampland criteria", that severely restrict the types of cosmological dynamics they can sustain. The first criterion states that the (multi-field) effective field theory description is only valid over a field displacement $\Delta \phi \leq \Delta \sim \mathcal O(1)$ (in units where the Planck mass is 1), measured as a distance in the target space geometry. A second, more recent, criterion asserts that, whenever the potential $V$ is positive, its slope must be bounded from below, and suggests $|\nabla V| / V \geq c \sim \mathcal O(1)$. A recent analysis concluded that these two conditions taken together practically rule out slow-roll models of inflation. In this note we show that the two conditions rule out inflationary backgrounds that follow geodesic trajectories in field space, but not those following curved, non-geodesic, trajectories (which are parametrized by a non-vanishing bending rate $\Omega$ of the multi-field trajectory). We derive a universal lower bound on $\Omega$ (relative to the Hubble parameter $H$) as a function of $\Delta, c$ and the number of efolds $N_e$, assumed to be at least of order 60. If later studies confirm $c$ and $\Delta$ to be strictly $\mathcal O(1)$, the bound implies strong turns with $\Omega / H \geq 3 N_e \sim 180$. Slow-roll inflation in the landscape is not ruled out, but it is strongly multi-field.Comment: v1: 15 pages; v2: 16 pages, references added, improved discussions, version accepted for publication in JCA

Gauge-Higgs unification on the brane

From the quantum field theory point of view, matter and gauge fields are generally expected to be localised around branes or topological defects occurring in extra dimensions. Here I discuss a simple scenario where, by starting with a five dimensional SU(3) gauge theory, we end up with several 4-D parallel branes with localised "chiral" fermions and gauge fields to them. I will show that it is possible to reproduce the electroweak model confined to a single brane, allowing a simple and geometrical approach to the fermion hierarchy problem. Some nice results of this construction are: Gauge and Higgs fields are unified at the 5-D level; and new particles are predicted: a left-handed neutrino of zero hypercharge, and a massive vector field coupling together the new neutrino to other left-handed leptons.Comment: Contribution to the proceedings of the RTN workshop "The Quest for Unification: Theory Confronts Experiment", Corfu, Greece, Sept 11-18, 200

Sensitivity-based multistep MPC for embedded systems

In model predictive control (MPC), an optimization problem is solved every sampling instant to determine an optimal control for a physical system. We aim to accelerate this procedure for fast systems applications and address the challenge of implementing the resulting MPC scheme on an embedded system with limited computing power. We present the sensitivity-based multistep MPC, a strategy which considerably reduces the computing requirements in terms of floating point operations (FLOPs), compared to a standard MPC formulation, while fulfilling closed- loop performance expectations. We illustrate by applying the method to a DC-DC converter model and show how a designer can optimally trade off closed-loop performance considerations with computing requirements in order to fit the controller into a resource-constrained embedded system