Combining type I and type II seesaw mechanisms in the minimal 3-3-1 model

The minimal 3-3-1 model is perturbative until energies around 4-5TeV, posing a challenge to generate neutrino masses at eV scale, mainly if one aims to take advantage of the seesaw mechanism. As a means to circumvent this problem we propose a modification of the model such that it accommodates the type I and type II seesaw mechanisms altogether. We show that the conjunction of both mechanisms yield a neutrino mass expression suppressed by a high power of the cutoff scale, $M^5$, in its denominator. With such a suppression term we naturally obtain neutrino masses at eV scale when $M$ is around few TeV. We also investigate the size of lepton flavor violation through the process $\mu \rightarrow e\gamma$.Comment: about 15 pages, no figure

Finite type invariants of 3-manifolds

A theory of finite type invariants for arbitrary compact oriented 3-manifolds is proposed, and illustrated through many examples arising from both classical and quantum topology. The theory is seen to be highly non-trivial even for manifolds with large first betti number, encompassing much of the complexity of Ohtsuki's theory for homology spheres. (For example, it is seen that the quantum SO(3) invariants, though not of finite type, are determined by finite type invariants.) The algebraic structure of the set of all finite type invariants is investigated, along with a combinatorial model for the theory in terms of trivalent "Feynman diagrams".Comment: Final version for publication, with figures. The most significant changes from the original posted version are in the exposition of section 3 (on the Conway polynomial) and section 4 (on quantum invariants

Flux Vacua Attractors in Type II on SU(3)xSU(3) Structure

We summarize and extend our work on flux vacua attractors in generalized compactifications. After reviewing the attractor equations for the heterotic string on SU(3) structure manifolds, we study attractors for N=1 vacua in type IIA/B on SU(3)xSU(3) structure spaces. In the case of vanishing RR flux, we find attractor equations that encode Minkowski vacua only (and which correct a previous normalization error). In addition to our previous considerations, here we also discuss the case of nonzero RR flux and the possibility of attractors for AdS vacua.Comment: 10 pages, contribution to the proceedings of the 4th RTN workshop "Forces Universe", Varna, September 200

Ramsey-type theorems for lines in 3-space

We prove geometric Ramsey-type statements on collections of lines in 3-space. These statements give guarantees on the size of a clique or an independent set in (hyper)graphs induced by incidence relations between lines, points, and reguli in 3-space. Among other things, we prove that: (1) The intersection graph of n lines in R^3 has a clique or independent set of size Omega(n^{1/3}). (2) Every set of n lines in R^3 has a subset of n^{1/2} lines that are all stabbed by one line, or a subset of Omega((n/log n)^{1/5}) such that no 6-subset is stabbed by one line. (3) Every set of n lines in general position in R^3 has a subset of Omega(n^{2/3}) lines that all lie on a regulus, or a subset of Omega(n^{1/3}) lines such that no 4-subset is contained in a regulus. The proofs of these statements all follow from geometric incidence bounds -- such as the Guth-Katz bound on point-line incidences in R^3 -- combined with Tur\'an-type results on independent sets in sparse graphs and hypergraphs. Although similar Ramsey-type statements can be proved using existing generic algebraic frameworks, the lower bounds we get are much larger than what can be obtained with these methods. The proofs directly yield polynomial-time algorithms for finding subsets of the claimed size.Comment: 18 pages including appendi

Finite type invariants of rational homology 3-spheres

We consider the rational vector space generated by all rational homology spheres up to orientation-preserving homeomorphism, and the filtration defined on this space by Lagrangian-preserving rational homology handlebody replacements. We identify the graded space associated with this filtration with a graded space of augmented Jacobi diagrams