6,066 research outputs found
Liouville Type Models in Group Theory Framework. I. Finite-Dimensional Algebras
In the series of papers we represent the ``Whittaker'' wave functional of
-dimensional Liouville model as a correlator in -dimensional theory
of the sine-Gordon type (for and ). Asypmtotics of this wave function
is characterized by the Harish-Chandra function, which is shown to be a product
of simple -function factors over all positive roots of the
corresponding algebras (finite-dimensional for and affine for ).
This is in nice correspondence with the recent results on 2- and 3-point
correlators in Liouville model, where emergence of peculiar
double-periodicity is observed. The Whittaker wave functions of
-dimensional non-affine ("conformal") Toda type models are given by simple
averages in the dimensional theories of the affine Toda type. This
phenomenon is in obvious parallel with representation of the free-field wave
functional, which is originally a Gaussian integral over interior of a
-dimensional disk with given boundary conditions, as a (non-local)
quadratic integral over the -dimensional boundary itself. In the present
paper we mostly concentrate on the finite-dimensional case. The results for
finite-dimensional "Iwasawa" Whittaker functions were known, and we present
their survey. We also construct new "Gauss" Whittaker functions.Comment: 47 pages, LaTe
Lattice Gauge Fields Topology Uncovered by Quaternionic sigma-model Embedding
We investigate SU(2) gauge fields topology using new approach, which exploits
the well known connection between SU(2) gauge theory and quaternionic
projective sigma-models and allows to formulate the topological charge density
entirely in terms of sigma-model fields. The method is studied in details and
for thermalized vacuum configurations is shown to be compatible with
overlap-based definition. We confirm that the topological charge is distributed
in localized four dimensional regions which, however, are not compatible with
instantons. Topological density bulk distribution is investigated at different
lattice spacings and is shown to possess some universal properties.Comment: revtex4, 19 pages (24 ps figures included); replaced to match the
published version, to appear in PRD; minor changes, references adde
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