84,163 research outputs found
Deformations and stability in complex hyperbolic geometry
This paper concerns with deformations of noncompact complex hyperbolic
manifolds (with locally Bergman metric), varieties of discrete representations
of their fundamental groups into and the problem of (quasiconformal)
stability of deformations of such groups and manifolds in the sense of L.Bers
and D.Sullivan.
Despite Goldman-Millson-Yue rigidity results for such complex manifolds of
infinite volume, we present different classes of such manifolds that allow
non-trivial (quasi-Fuchsian) deformations and point out that such flexible
manifolds have a common feature being Stein spaces. While deformations of
complex surfaces from our first class are induced by quasiconformal
homeomorphisms, non-rigid complex surfaces (homotopy equivalent to their
complex analytic submanifolds) from another class are quasiconformally
unstable, but nevertheless their deformations are induced by homeomorphisms
Exploring the Vacuum Geometry of N=1 Gauge Theories
Using techniques of algorithmic algebraic geometry, we present a new and
efficient method for explicitly computing the vacuum space of N=1 gauge
theories. We emphasize the importance of finding special geometric properties
of these spaces in connecting phenomenology to guiding principles descending
from high-energy physics. We exemplify the method by addressing various
subsectors of the MSSM. In particular the geometry of the vacuum space of
electroweak theory is described in detail, with and without right-handed
neutrinos. We discuss the impact of our method on the search for evidence of
underlying physics at a higher energy. Finally we describe how our results can
be used to rule out certain top-down constructions of electroweak physics.Comment: 35 pages, 2 figures, LaTe
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