Twisted Alexander polynomials of Plane Algebraic Curves

We consider the Alexander polynomial of a plane algebraic curve twisted by a linear representation. We show that it divides the product of the polynomials of the singularity links, for unitary representations. Moreover, their quotient is given by the determinant of its Blanchfield intersection form. Specializing in the classical case, this gives a geometrical interpretation of Libgober's divisibility Theorem. We calculate twisted polynomials for some algebraic curves and show how they can detect Zariski pairs of equivalent Alexander polynomials and that they are sensitive to nodal degenerations.Comment: 16 pages, no figure

Lepton Flavor Violation in Little Higgs Models

We report on our study of the LFV processes \mu \to e\gamma, \mu\to eee and \mu \to e conversion in the context of Little Higgs models. Specifically we examine the Littlest Higgs with T-parity (LHT) and the Simplest Little Higgs (SLH) as examples of a Product group and Simple group Little Higgs models respectively. The necessary Feynman rules for both models are obtained in the 't Hooft Feynman Gauge up to order v^2/f^2 and predictions for the branching ratios and conversion rates of the LFV processes are calculated to leading order (one-loop level). Comparison with current experimental constraints show that there is some tension and, in order to be within the limits, one requires a higher breaking scale f, alignment of the heavy and light lepton sectors or almost degenerate heavy lepton masses. These constraints are more demanding in the SLH than in the LHT case.Comment: 6 pages, 3 figures, to appear in Proceedings of the XXXIII Intl. Conf. of Theoretical Physics, "Matter to the Deepest", Ustron, Poland, September 11-16, 2009; v2: comments and references adde