917 research outputs found
Explicit Character Formulae for Positive Energy UIRs of D=4 Conformal Supersymmetry
This paper continues the project of constructing the character formulae for
the positive energy unitary irreducible representations of the N-extended D=4
conformal superalgebras su(2,2/N). In the first paper we gave the bare
characters which represent the defining odd entries of the characters. Now we
give the full explicit character formulae for N=1 and for several important
examples for N=2 and N=4.Comment: 48 pages, TeX with Harvmac, overlap in preliminaries with
arXiv:hep-th/0406154; some comments and references adde
On a "New" Deformation of GL(2)
We refute a recent claim in the literature of a "new" quantum deformation of
GL(2).Comment: 4 pages, LATE
Duality and Representations for New Exotic Bialgebras
We find the exotic matrix bialgebras which correspond to the two
non-triangular nonsingular 4x4 R-matrices in the classification of Hietarinta,
namely, R_{S0,3} and R_{S1,4}. We find two new exotic bialgebras S03 and S14
which are not deformations of the of the classical algebras of functions on
GL(2) or GL(1|1). With this we finalize the classification of the matrix
bialgebras which unital associative algebras generated by four elements. We
also find the corresponding dual bialgebras of these new exotic bialgebras and
study their representation theory in detail. We also discuss in detail a
special case of R_{S1,4} in which the corresponding algebra turns out to be a
special case of the two-parameter quantum group deformation GL_{p,q}(2).Comment: 33 pages, LaTeX2e, using packages: cite,amsfonts,amsmath,subeqn;
reference updated; v3: corrections in subsection 3.
Exotic Bialgebra S03: Representations, Baxterisation and Applications
The exotic bialgebra S03, defined by a solution of the Yang-Baxter equation,
which is not a deformation of the trivial, is considered. Its FRT dual algebra
is studied. The Baxterisation of the dual algebra is given in two
different parametrisations. The finite-dimensional representations of
are considered. Diagonalisations of the braid matrices are used to yield
remarkable insights concerning representations of the L-algebra and to
formulate the fusion of finite-dimensional representations. Possible
applications are considered, in particular, an exotic eight-vertex model and an
integrable spin-chain model.Comment: 24 pages, Latex; V2: revised subsection 4.1, added 9 references, to
appear in Annales Henri Poincare in the volume dedicated to D. Arnaudo
Character Formulae and Partition Functions in Higher Dimensional Conformal Field Theory
A discussion of character formulae for positive energy unitary irreducible
representations of the the conformal group is given, employing Verma modules
and Weyl group reflections. Product formulae for various conformal group
representations are found. These include generalisations of those found by
Flato and Fronsdal for SO(3,2). In even dimensions the products for free
representations split into two types depending on whether the dimension is
divisible by four or not.Comment: 43 pages, uses harvmac,version 2 2 references added, minor typos
correcte
Anomalies, Unparticles, and Seiberg Duality
We calculate triangle anomalies for fermions with non-canonical scaling
dimensions. The most well known example of such fermions (aka unfermions)
occurs in Seiberg duality where the matching of anomalies (including mesinos
with scaling dimensions between 3/2 and 5/2) is a crucial test of duality. By
weakly gauging the non-local action for an unfermion, we calculate the one-loop
three-current amplitude. Despite the fact that there are more graphs with more
complicated propagators and vertices, we find that the calculation can be
completed in a way that nearly parallels the usual case. We show that the
anomaly factor for fermionic unparticles is independent of the scaling
dimension and identical to that for ordinary fermions. This can be viewed as a
confirmation that unparticle actions correctly capture the physics of conformal
fixed point theories like Banks-Zaks or SUSY QCD.Comment: 13 pages, 1 figur
On the Unitarity of D=9,10,11 Conformal Supersymmetry
We consider the unitarity of D=9,10,11 conformal supersymmetry using the
recently established classification of the UIRs of the superalgebras
osp(1|2n,R).Comment: 7 pages, LATEX2e{czjphys} (amsmath,amssymb); v3: important
corrections, Plenary talk by VKD at the XIII Colloquium "Quantum Groups and
Integrable Systems", Prague, 17-19.6.2004; to appear in Czech. J. Phys.; v4:
small corrections to coincide with journal versio
A Jordanian quantum two-photon/Schrodinger algebra
A non-standard quantum deformation of the two-photon algebra is
constructed, and its quantum universal R-matrix is given. Representations of
this new quantum algebra are studied on the Fock space and translated into
Fock-Bargmann realizations that provide a direct formalism for the definition
of deformed states of light. Finally, the isomorphism between and the
(1+1) Schr\"odinger algebra is used to introduce a new (non-standard) Hopf
algebra deformation of this latter symmetry algebra.Comment: 12 pages, LaTeX, misprints correcte
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