1,284 research outputs found
Toda equations associated with loop groups of complex classical Lie groups
A Toda equation is specified by a choice of a Lie group and a -gradation of its Lie algebra. The Toda equations associated with loop groups
of complex classical Lie groups, whose Lie algebras are endowed with integrable
-gradations with finite dimensional grading subspaces, are described
in an explicit form.Comment: 39 page
Maximally nonabelian Toda systems
A detailed consideration of the maximally nonabelian Toda systems based on
the classical semisimple Lie groups is given. The explicit expressions for the
general solution of the corresponding equations are obtained.Comment: 28 pages, LaTeX file. A few references and appendix B are added; this
version will appear in Nuclear Physics
On the supersymmetric vacua of the Veneziano-Wosiek model
We study the supersymmetric vacua of the Veneziano-Wosiek model in sectors
with fermion number F=2, 4 at finite 't Hooft coupling lambda. We prove that
for F=2 there are two zero energy vacua for lambda > lambda_c = 1 and none
otherwise. We give the analytical expressions of both vacua. One of them was
previously known, the second one is obtained by solving the cohomology of the
supersymmetric charges. At F=4 we compute the would-be supersymmetric vacua at
high order in the the strong coupling expansion and provide strong support to
the conclusion that lambda = 1 is a critical point in this sector too. It
separates a strong coupling phase with two symmetric vacua from a weak coupling
phase with positive spectrum.Comment: 17 pages, 2 eps figure
Highest -Weight Representations and Functional Relations
We discuss highest -weight representations of quantum loop algebras and
the corresponding functional relations between integrability objects. In
particular, we compare the prefundamental and -oscillator representations of
the positive Borel subalgebras of the quantum group for arbitrary values of . Our article has partially
the nature of a short review, but it also contains new results. These are the
expressions for the -operators, and the exact relationship between different
representations, as a byproduct resulting in certain conclusions about
functional relations
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