5,378 research outputs found
Classical r-matrices via semidualisation
We study the interplay between double cross sum decompositions of a given Lie
algebra and classical r-matrices for its semidual. For a class of Lie algebras
which can be obtained by a process of generalised complexification we derive an
expression for classical r-matrices of the semidual Lie bialgebra in terms of
the data which determines the decomposition of the original Lie algebra.
Applied to the local isometry Lie algebras arising in three-dimensional
gravity, decomposition and semidualisation yields the main class of non-trivial
r-matrices for the Euclidean and Poincare group in three dimensions. In
addition, the construction links the r-matrices with the Bianchi classification
of three dimensional real Lie algebras.Comment: 21 pages, 1 figure, typos correcte
Classical r-matrices for the generalised Chern-Simons formulation of 3d gravity
We study the conditions for classical r-matrices to be compatible with the
generalised Chern-Simons action for 3d gravity. Compatibility means solving the
classical Yang-Baxter equations with a prescribed symmetric part for each of
the real Lie algebras and bilinear pairings arising in the generalised
Chern-Simons action. We give a new construction of r-matrices via a generalised
complexification and derive a non-linear set of matrix equations determining
the most general compatible r-matrix. We exhibit new families of solutions and
show that they contain known solutions for special parameter valuesComment: 20 pages, minor corrections and comments added in v
On the phase structure and thermodynamics of QCD
We discuss the phase structure and thermodynamics of QCD by means of
dynamical chiral effective models. Quark and meson fluctuations are included
via the functional renormalization group. We study the influence of confinement
in addition to the impact of fluctuations by comparing the results of the
chiral models to their Polyakov-loop extended versions. Furthermore, we discuss
the mass sensitivity of the phase structure and thermodynamics and find
interesting modifications close to the chiral limit.Comment: 13 pages, 11 figures; Appendix added; published versio
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