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

Finitely presented lattice-ordered abelian groups with order-unit

Let $G$ be an $\ell$-group (which is short for ``lattice-ordered abelian group''). Baker and Beynon proved that $G$ is finitely presented iff it is finitely generated and projective. In the category $\mathcal U$ of {\it unital} $\ell$-groups---those $\ell$-groups having a distinguished order-unit $u$---only the $(\Leftarrow)$-direction holds in general. Morphisms in $\mathcal U$ are {\it unital $\ell$-homomorphisms,} i.e., hom\-o\-mor\-phisms that preserve the order-unit and the lattice structure. We show that a unital $\ell$-group $(G,u)$ is finitely presented iff it has a basis, i.e., $G$ is generated by an abstract Schauder basis over its maximal spectral space. Thus every finitely generated projective unital $\ell$-group has a basis $\mathcal B$. As a partial converse, a large class of projectives is constructed from bases satisfying $\bigwedge\mathcal B\not=0$. Without using the Effros-Handelman-Shen theorem, we finally show that the bases of any finitely presented unital $\ell$-group $(G,u)$ provide a direct system of simplicial groups with 1-1 positive unital homomorphisms, whose limit is $(G,u)$