368 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
Cyclotomic shuffles
Analogues of 1-shuffle elements for complex reflection groups of type
are introduced. A geometric interpretation for in terms
of rotational permutations of polygonal cards is given. We compute the
eigenvalues, and their multiplicities, of the 1-shuffle element in the algebra
of the group . Considering shuffling as a random walk on the group
, we estimate the rate of convergence to randomness of the
corresponding Markov chain. We report on the spectrum of the 1-shuffle analogue
in the cyclotomic Hecke algebra for and small
Super Self-Duality as Analyticity in Harmonic Superspace
A twistor correspondence for the self-duality equations for supersymmetric
Yang-Mills theories is developed. Their solutions are shown to be encoded in
analytic harmonic superfields satisfying appropriate generalised Cauchy-Riemann
conditions. An action principle yielding these conditions is presented.Comment: 1 + 8 pages, plaintex, CERN-TH.6653/9
Quantization of chiral antisymmetric tensor fields
Chiral antisymmetric tensor fields can have chiral couplings to quarks and
leptons. Their kinetic terms do not mix different representations of the
Lorentz symmetry and a local mass term is forbidden by symmetry. The chiral
couplings to the fermions are asymptotically free, opening interesting
perspectives for a possible solution to the gauge hierarchy problem. We argue
that the interacting theory for such fields can be consistently quantized, in
contrast to the free theory which is plagued by unstable solutions. We suggest
that at the scale where the chiral couplings grow large the electroweak
symmetry is spontaneously broken and a mass term for the chiral tensors is
generated non-perturbatively. Massive chiral tensors correspond to massive spin
one particles that do not have problems of stability. We also propose an
equivalent formulation in terms of gauge fields.Comment: additional material, concentrating on interactions with chiral
fermions, 38 pages, 1 figur
Fusion Procedure for Cyclotomic Hecke Algebras
A complete system of primitive pairwise orthogonal idempotents for cyclotomic
Hecke algebras is constructed by consecutive evaluations of a rational function
in several variables on quantum contents of multi-tableaux. This function is a
product of two terms, one of which depends only on the shape of the
multi-tableau and is proportional to the inverse of the corresponding Schur
element
On representations of complex reflection groups G(m,1,n)
An inductive approach to the representation theory of the chain of the
complex reflection groups G(m,1,n) is presented. We obtain the Jucys-Murphy
elements of G(m,1,n) from the Jucys--Murphy elements of the cyclotomic Hecke
algebra, and study their common spectrum using representations of a degenerate
cyclotomic affine Hecke algebra. Representations of G(m,1,n) are constructed
with the help of a new associative algebra whose underlying vector space is the
tensor product of the group ring of G(m,1,n) with a free associative algebra
generated by the standard m-tableaux.Comment: 18 page
BRST operator for quantum Lie algebras and differential calculus on quantum groups
For a Hopf algebra A, we define the structures of differential complexes on
two dual exterior Hopf algebras: 1) an exterior extension of A and 2) an
exterior extension of the dual algebra A^*. The Heisenberg double of these two
exterior Hopf algebras defines the differential algebra for the Cartan
differential calculus on A. The first differential complex is an analog of the
de Rham complex. In the situation when A^* is a universal enveloping of a Lie
(super)algebra the second complex coincides with the standard complex. The
differential is realized as an (anti)commutator with a BRST- operator Q. A
recurrent relation which defines uniquely the operator Q is given. The BRST and
anti-BRST operators are constructed explicitly and the Hodge decomposition
theorem is formulated for the case of the quantum Lie algebra U_q(gl(N)).Comment: 20 pages, LaTeX, Lecture given at the Workshop on "Classical and
Quantum Integrable Systems", 8 - 11 January, Protvino, Russia; corrected some
typo
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