750 research outputs found
Conserved currents for unconventional supersymmetric couplings of self-dual gauge fields
Self-dual gauge potentials admit supersymmetric couplings to higher-spin
fields satisfying interacting forms of the first order Dirac--Fierz equation.
The interactions are governed by conserved currents determined by
supersymmetry. These super-self-dual Yang-Mills systems provide on-shell
supermultiplets of arbitrarily extended super-Poincar\'e algebras; classical
consistency not setting any limit on the extension N. We explicitly display
equations of motion up to the extension. The stress tensor, which
vanishes for the self-duality equations, not only gets resurrected
when , but is then a member of a conserved multiplet of gauge-invariant
tensors.Comment: 6 pages, latex fil
Quantum dynamics of , supergravity compensator
A new superfield theory in flat superspace is suggested. It
describes dynamics of supergravity compensator and can be considered as a
low-energy limit for , superfield supergravity. The theory is shown
to be renormalizable in infrared limit and infrared free. A quantum effective
action is investigated in infrared domain
Linear and nonlinear realizations of superbranes
The coordinate transformations which establish the direct relationship
between the actions of linear and nonlinear realizations of supermembranes are
proposed. It is shown that the Rocek-Tseytlin constraint known in the framework
of the linear realization of the theory is simply equivalent to a limit of a
"pure" nonlinear realization in which the field describing the massive mode of
the supermembrane puts to zero.Comment: 8 pages, LaTeX + espcrc2.sty The talk given at the D. Volkov Memorial
Conference SQFT, July, 25-29, 200
Diagonal reduction algebras of \gl type
Several general properties, concerning reduction algebras - rings of
definition and algorithmic efficiency of the set of ordering relations - are
discussed. For the reduction algebras, related to the diagonal embedding of the
Lie algebra into , we establish a stabilization
phenomenon and list the complete sets of defining relations.Comment: 24 pages, no figure
R-matrices in Rime
We replace the ice Ansatz on matrix solutions of the Yang-Baxter equation by
a weaker condition which we call "rime". Rime solutions include the standard
Drinfeld-Jimbo R-matrix. Solutions of the Yang--Baxter equation within the rime
Ansatz which are maximally different from the standard one we call "strict
rime". A strict rime non-unitary solution is parameterized by a projective
vector. We show that this solution transforms to the Cremmer-Gervais R-matrix
by a change of basis with a matrix containing symmetric functions in the
components of the parameterizing vector. A strict unitary solution (the rime
Ansatz is well adapted for taking a unitary limit) is shown to be equivalent to
a quantization of a classical "boundary" r-matrix of Gerstenhaber and
Giaquinto. We analyze the structure of the elementary rime blocks and find, as
a by-product, that all non-standard R-matrices of GL(1|1)-type can be uniformly
described in a rime form.
We discuss then connections of the classical rime solutions with the Bezout
operators. The Bezout operators satisfy the (non-)homogeneous associative
classical Yang--Baxter equation which is related to the Rota-Baxter operators.
We classify the rime Poisson brackets: they form a 3-dimensional pencil. A
normal form of each individual member of the pencil depends on the discriminant
of a certain quadratic polynomial. We also classify orderable quadratic rime
associative algebras.
For the standard Drinfeld-Jimbo solution, there is a choice of the
multiparameters, for which it can be non-trivially rimed. However, not every
Belavin-Drinfeld triple admits a choice of the multiparameters for which it can
be rimed. We give a minimal example.Comment: 50 pages, typos correcte
The matreoshka of supersymmetric self-dual theories
Extended super self-dual systems have a structure reminiscent of a
``matreoshka''. For instance, solutions for N=0 are embedded in solutions for
N=1, which are in turn embedded in solutions for N=2, and so on. Consequences
of this phenomenon are explored. In particular, we present an explicit
construction of local solutions of the higher-N super self-duality equations
starting from any N=0 self-dual solution. Our construction uses N=0 solution
data to produce N=1 solution data, which in turn yields N=2 solution data, and
so on; each stage introducing a dependence of the solution on sufficiently many
additional arbitrary functions to yield the most general supersymmetric
solution having the initial N=0 solution as the helicity +1 component. The
problem of finding the general local solution of the super self-duality
equations therefore reduces to finding the general solution of the usual (N=0)
self-duality equations. Another consequence of the matreoshka phenomenon is the
vanishing of many conserved currents, including the supercurrents, for super
self-dual systems.Comment: 19 pages, Bonn-HE-93-2
Braidings of Tensor Spaces
Let be a braided vector space, that is, a vector space together with a
solution of the Yang--Baxter equation.
Denote . We associate to a solution
of the Yang--Baxter equation on
the tensor space . The correspondence is functorial with respect to .Comment: 10 pages, no figure
On Inflation Rules for Mosseri-Sadoc Tilings
We give the inflation rules for the decorated Mosseri-Sadoc tiles in the
projection class of tilings . Dehn invariants related to the
stone inflation of the Mosseri-Sadoc tiles provide eigenvectors of the
inflation matrix with eigenvalues equal to and
.Comment: LaTeX file, 4(3) pages + 7 figures (FIG1.gif, FIG2.gif,... FIH7.gif)
and a style file (icqproc.sty
Drinfeld-Jimbo quantum Lie algebra
Quantum Lie algebras related to multi-parametric Drinfeld-Jimbo -matrices
of type are classified.Comment: 9 page
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