Low-energy effective theory for a Randall-Sundrum scenario with a moving bulk brane

We derive the low-energy effective theory of gravity for a generalized Randall-Sundrum scenario, allowing for a third self-gravitating brane to live in the 5D bulk spacetime. At zero order the 5D spacetime is composed of two slices of anti-de Sitter spacetime, each with a different curvature scale, and the 5D Weyl tensor vanishes. Two boundary branes are at the fixed points of the orbifold whereas the third brane is free to move in the bulk. At first order, the third brane breaks the otherwise continuous evolution of the projection of the Weyl tensor normal to the branes. We derive a junction condition for the projected Weyl tensor across the bulk brane, and combining this constraint with the junction condition for the extrinsic curvature tensor, allows us to derive the first-order field equations on the middle brane. The effective theory is a generalized Brans-Dicke theory with two scalar fields. This is conformally equivalent to Einstein gravity and two scalar fields, minimally coupled to the geometry, but nonminimally coupled to matter on the three branes.Comment: 16 pages, 1 figure, typos correcte

Loop and Path Spaces and Four-Dimensional BF Theories: Connections, Holonomies and Observables

We study the differential geometry of principal G-bundles whose base space is the space of free paths (loops) on a manifold M. In particular we consider connections defined in terms of pairs (A,B), where A is a connection for a fixed principal bundle P(M,G) and B is a 2-form on M. The relevant curvatures, parallel transports and holonomies are computed and their expressions in local coordinates are exhibited. When the 2-form B is given by the curvature of A, then the so-called non-abelian Stokes formula follows. For a generic 2-form B, we distinguish the cases when the parallel transport depends on the whole path of paths and when it depends only on the spanned surface. In particular we discuss generalizations of the non-abelian Stokes formula. We study also the invariance properties of the (trace of the) holonomy under suitable transformation groups acting on the pairs (A,B). In this way we are able to define observables for both topological and non-topological quantum field theories of the BF type. In the non topological case, the surface terms may be relevant for the understanding of the quark-confinement problem. In the topological case the (perturbative) four-dimensional quantum BF-theory is expected to yield invariants of imbedded (or immersed) surfaces in a 4-manifold M.Comment: TeX, 39 page

Three-dimensional BF Theories and the Alexander-Conway Invariant of Knots

We study 3-dimensional BF theories and define observables related to knots and links. The quantum expectation values of these observables give the coefficients of the Alexander-Conway polynomial.Comment: 32 pages (figures available upon request); LaTe

Bounds on Dark Matter Interactions with Electroweak Gauge Bosons

We investigate scenarios in which dark matter interacts with the Standard Model primarily through electroweak gauge bosons. We employ an effective field theory framework wherein the Standard Model and the dark matter particle are the only light states in order to derive model-independent bounds. Bounds on such interactions are derived from dark matter production by weak boson fusion at the LHC, indirect detection searches for the products of dark matter annihilation and from the measured invisible width of the $Z^0$. We find that limits on the UV scale, $\Lambda$, reach weak scale values for most operators and values of the dark matter mass, thus probing the most natural scenarios in the WIMP dark matter paradigm. Our bounds suggest that light dark matter (m_{\chi}\lsim m_Z/2 or m_{\chi}\lsim 100-200\gev, depending on the operator) cannot interact only with the electroweak gauge bosons of the Standard Model, but rather requires additional operator contributions or dark sector structure to avoid overclosing the universe.Comment: 45 pages, 26 figure

Loop observables for BF theories in any dimension and the cohomology of knots

A generalization of Wilson loop observables for BF theories in any dimension is introduced in the Batalin-Vilkovisky framework. The expectation values of these observables are cohomology classes of the space of imbeddings of a circle. One of the resulting theories discussed in the paper has only trivalent interactions and, irrespective of the actual dimension, looks like a 3-dimensional Chern-Simons theory.Comment: 13 page

Legge e sicurezza

Starting from the analysis of the first book of De libero arbitrio, the Italian philosopher Sergio Cotta (1921-2007) explores the relationship between law, morality and safety in Augustine’s thought. According to Cotta, Lib. arb. I contains implicitly a complete typology of the four normative judgments used in jurisprudence, philosophy of law and legal science: (i) judgments of legality; (ii) judgments of validity; (iii) judgments of purpose; (iv) judgments of morality. The analysis of the relationship between these four types of normative judgments allows us to interpret correctly Augustine’s most famous sentence: mihi lex esse non videtur quae iusta non fuerit