Warped 5D Standard Model Consistent with EWPT

For a 5D Standard Model propagating in an AdS background with an IR localized Higgs, compatibility of bulk KK gauge modes with EWPT yields a phenomenologically unappealing KK spectrum (m > 12.5 TeV) and leads to a "little hierarchy problem". For a bulk Higgs the solution to the hierarchy problem reduces the previous bound only by sqrt(3). As a way out, models with an enhanced bulk gauge symmetry SU(2)_R x U(1)_(B-L) were proposed. In this note we describe a much simpler (5D Standard) Model, where introduction of an enlarged gauge symmetry is no longer required. It is based on a warped gravitational background which departs from AdS at the IR brane and a bulk propagating Higgs. The model is consistent with EWPT for a range of KK masses within the LHC reach.Comment: 7 pages, 3 figures. Based on talk given by M. Quiros at the Workshop on the Standard Model and Beyond - Cosmology, Corfu Summer Institute, Greece, August 29 - September 5, 201

Severi-Bouligand tangents, Frenet frames and Riesz spaces

It was recently proved that a compact set $X\subseteq \mathbb R^2$ has an outgoing Severi-Bouligand tangent vector $u\not=0$ at $x\in X$ iff some principal ideal of the Riesz space $\mathcal R(X)$ of piecewise linear functions on $X$ is not an intersection of maximal ideals. "Outgoing" means $X\cap [x,x+u]=\{x\}$. Suppose now $X\subseteq \mathbb{R}^n$ and some principal ideal of $\mathcal R(X)$ is not an intersection of maximal ideals. We prove that this is equivalent to saying that $X$ contains a sequence $\{x_i\}$ whose Frenet $k$-frame $(u_1,\ldots,u_k)$ is an outgoing Severi-Bouligand tangent of $X$. When the $\{x_i\}$ are taken as sample points of a smooth curve $\gamma,$ the Frenet $k$-frames of $\{x_i\}$ and of $\gamma$ coincide. The computation of Frenet frames via sample sequences does not require the knowledge of any higher-order derivative of $\gamma$

Admissibility via Natural Dualities

It is shown that admissible clauses and quasi-identities of quasivarieties generated by a single finite algebra, or equivalently, the quasiequational and universal theories of their free algebras on countably infinitely many generators, may be characterized using natural dualities. In particular, axiomatizations are obtained for the admissible clauses and quasi-identities of bounded distributive lattices, Stone algebras, Kleene algebras and lattices, and De Morgan algebras and lattices.Comment: 22 pages; 3 figure

A general framework for product representations: bilattices and beyond

This paper studies algebras arising as algebraic semantics for logics used to model reasoning with incomplete or inconsistent information. In particular we study, in a uniform way, varieties of bilattices equipped with additional logic-related operations and their product representations. Our principal result is a very general product representation theorem. Specifically, we present a syntactic procedure (called duplication) for building a product algebra out of a given base algebra and a given set of terms. The procedure lifts functorially to the generated varieties and leads, under specified sufficient conditions, to a categorical equivalence between these varieties. When these conditions are satisfied, a very tight algebraic relationship exists between the base variety and the enriched variety. Moreover varieties arising as duplicates of a common base variety are automatically categorically equivalent to each other. Two further product representation constructions are also presented; these are in the same spirit as our main theorem and extend the scope of our analysis. Our catalogue of applications selects varieties for which product representations have previously been obtained one by one, or which are new. We also reveal that certain varieties arising from the modelling of quite different operations are categorically equivalent. Among the range of examples presented, we draw attention in particular to our systematic treatment of trilattices.Comment: 20 pages 2 table