42 research outputs found
Phenomenology of a light scalar: the dilaton
We make use of the language of non-linear realizations to analyze
electro-weak symmetry breaking scenarios in which a light dilaton emerges from
the breaking of a nearly conformal strong dynamics, and compare the
phenomenology of the dilaton to that of the well motivated light composite
Higgs scenario. We argue that -- in addition to departures in the
decay/production rates into massless gauge bosons mediated by the conformal
anomaly -- characterizing features of the light dilaton scenario (as well as
other scenarios admitting a light CP-even scalar not directly related to the
breaking of the electro-weak symmetry) are off-shell events at high invariant
mass involving two longitudinally polarized vector bosons and a dilaton, and
tree-level flavor violating processes. Accommodating both electro-weak
precision measurements and flavor constraints appears especially challenging in
the ambiguous scenario in which the Higgs and the dilaton fields strongly mix.
We show that warped higgsless models of electro-weak symmetry breaking are
explicit and tractable realizations of this limiting case.
The relation between the naive radion profile often adopted in the study of
holographic realizations of the light dilaton scenario and the actual dynamical
dilaton field is clarified in the Appendix.Comment: 21 page
Random matrix theory and symmetric spaces
In this review we discuss the relationship between random matrix theories and
symmetric spaces. We show that the integration manifolds of random matrix
theories, the eigenvalue distribution, and the Dyson and boundary indices
characterizing the ensembles are in strict correspondence with symmetric spaces
and the intrinsic characteristics of their restricted root lattices. Several
important results can be obtained from this identification. In particular the
Cartan classification of triplets of symmetric spaces with positive, zero and
negative curvature gives rise to a new classification of random matrix
ensembles. The review is organized into two main parts. In Part I the theory of
symmetric spaces is reviewed with particular emphasis on the ideas relevant for
appreciating the correspondence with random matrix theories. In Part II we
discuss various applications of symmetric spaces to random matrix theories and
in particular the new classification of disordered systems derived from the
classification of symmetric spaces. We also review how the mapping from
integrable Calogero--Sutherland models to symmetric spaces can be used in the
theory of random matrices, with particular consequences for quantum transport
problems. We conclude indicating some interesting new directions of research
based on these identifications.Comment: 161 pages, LaTeX, no figures. Revised version with major additions in
the second part of the review. Version accepted for publication on Physics
Report
Felix Alexandrovich Berezin and his work
This is a survey of Berezin's work focused on three topics: representation
theory, general concept of quantization, and supermathematics.Comment: LaTeX, 27 page
Geometry of GL_n(C) on infinity: complete collineations, projective compactifications, and universal boundary
Consider a finite dimensional (generally reducible) polynomial representation
\rho of GL_n. A projective compactification of GL_n is the closure of
\rho(GL_n) in the space of all operators defined up to a factor (this class of
spaces can be characterized as equivariant projective normal compactifications
of GL_n). We give an expicit description for all projective compactifications.
We also construct explicitly (in elementary geometrical terms) a universal
object for all projective compactifications of GL_n.Comment: 24 pages, corrected varian