37 research outputs found
Superembedding methods for 4d N=1 SCFTs
We extend SO(4,2) covariant lightcone embedding methods of four-dimensional
CFTs to N=1 superconformal field theory (SCFT). Manifest superconformal
SU(2,2|1) invariance is achieved by realizing 4D superconformal space as a
surface embedded in the projective superspace spanned by certain complex chiral
supermatrices. Because SU(2,2|1) acts linearly on the ambient space, the
constraints on correlators implied by superconformal Ward identities are
automatically solved in this formalism. Applications include new, compact
expressions for correlation functions containing one anti-chiral superfield and
arbitrary chiral superfield insertions, and manifestly invariant expressions
for the superconformal cross-ratios that parametrize the four-point function of
two chiral and two anti-chiral fields. Superconformal expressions for the
leading singularities in the OPE of chiral and anti-chiral operators are also
given. Because of covariance, our expressions are valid in any superconformally
flat background, e.g., AdS_4 or R times S^3.Comment: 33 pages, clarification of constraints, version to appear in PR
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.
On the biparametric quantum deformation of GL(2) x GL(1)
We study the biparametric quantum deformation of GL(2) x GL(1) and exhibit
its cross-product structure. We derive explictly the associated dual algebra,
i.e., the quantised universal enveloping algebra employing the R-matrix
procedure. This facilitates construction of a bicovariant differential calculus
which is also shown to have a cross-product structure. Finally, a Jordanian
analogue of the deformation is presented as a cross-product algebra.Comment: 16 pages LaTeX, published in JM
RTT relations, a modified braid equation and noncommutative planes
With the known group relations for the elements of a quantum
matrix as input a general solution of the relations is sought without
imposing the Yang - Baxter constraint for or the braid equation for
. For three biparametric deformatios, and , the standard,the nonstandard and the
hybrid one respectively, or is found to depend, apart from the
two parameters defining the deformation in question, on an extra free parameter
,such that only for two values of , given explicitly for each case, one
has the braid equation. Arbitray corresponds to a class (conserving the
group relations independent of ) of the MQYBE or modified quantum YB
equations studied by Gerstenhaber, Giaquinto and Schak. Various properties of
the triparametric , and are
studied. In the larger space of the modified braid equation (MBE) even
can satisfy outside braid equation (BE)
subspace. A generalized, - dependent, Hecke condition is satisfied by each
3-parameter . The role of in noncommutative geometries of the
, and deformed planes is studied. K is found to
introduce a "soft symmetry breaking", preserving most interesting properties
and leading to new interesting ones. Further aspects to be explored are
indicated.Comment: Latex, 17 pages, minor change
Applications of Two-Body Dirac Equations to the Meson Spectrum with Three versus Two Covariant Interactions, SU(3) Mixing, and Comparison to a Quasipotential Approach
In a previous paper Crater and Van Alstine applied the Two Body Dirac
equations of constraint dynamics to the meson quark-antiquark bound states
using a relativistic extention of the Adler-Piran potential and compared their
spectral results to those from other approaches, ones which also considered
meson spectroscopy as a whole and not in parts. In this paper we explore in
more detail the differences and similarities in an important subset of those
approaches, the quasipotential approach. In the earlier paper, the
transformation properties of the quark-antiquark potentials were limited to a
scalar and an electromagnetic-like four vector, with the former accounting for
the confining aspects of the overall potential, and the latter the short range
portion. A part of that work consisted of developing a way in which the static
Adler-Piran potential was apportioned between those two different types of
potentials in addition to covariantization. Here we make a change in this
apportionment that leads to a substantial improvement in the resultant
spectroscopy by including a time-like confining vector potential over and above
the scalar confining one and the electromagnetic-like vector potential. Our fit
includes 19 more mesons than the earlier results and we modify the scalar
portion of the potential in such a way that allows this formalism to account
for the isoscalar mesons {\eta} and {\eta}' not included in the previous work.
Continuing the comparisons made in the previous paper with other approaches to
meson spectroscopy we examine in this paper the quasipotential approach of
Ebert, Faustov, and Galkin for a comparison with our formalism and spectral
results.Comment: Revisions of earlier versio
Tensor Operators for Uh(sl(2))
Tensor operators for the Jordanian quantum algebra Uh(sl(2)) are considered.
Some explicit examples of them, which are obtained in the boson or fermion
realization, are given and their properties are studied. It is also shown that
the Wigner-Eckart's theorem can be extended to Uh(sl(2)).Comment: 11pages, LaTeX, to be published in J. Phys.
Twist Deformation of the rank one Lie Superalgebra
The Drinfeld twist is applyed to deforme the rank one orthosymplectic Lie
superalgebra . The twist element is the same as for the Lie
algebra due to the embedding of the into the superalgebra .
The R-matrix has the direct sum structure in the irreducible representations of
. The dual quantum group is defined using the FRT-formalism. It
includes the Jordanian quantum group as subalgebra and Grassmann
generators as well.Comment: LaTeX, 9 page
Duality for Exotic Bialgebras
In the classification of Hietarinta, three triangular
-matrices lead, via the FRT formalism, to matrix bialgebras which are not
deformations of the trivial one. In this paper, we find the bialgebras which
are in duality with these three exotic matrix bialgebras. We note that the
duality of FRT is not sufficient for the construction of the bialgebras
in duality. We find also the quantum planes corresponding to these bialgebras
both by the Wess-Zumino R-matrix method and by Manin's method.Comment: 25 pages, LaTeX2e, using packages: cite, amsfonts, amsmath, subeq
Duality for the Jordanian Matrix Quantum Group
We find the Hopf algebra dual to the Jordanian matrix quantum group
. As an algebra it depends only on the sum of the two parameters
and is split in two subalgebras: (with three generators) and
(with one generator). The subalgebra is a central Hopf subalgebra of
. The subalgebra is not a Hopf subalgebra and its coalgebra
structure depends on both parameters. We discuss also two one-parameter special
cases: and . The subalgebra is a Hopf algebra and
coincides with the algebra introduced by Ohn as the dual of . The
subalgebra is isomorphic to as an algebra but has a
nontrivial coalgebra structure and again is not a Hopf subalgebra of
.Comment: plain TeX with harvmac, 16 pages, added Appendix implementing the ACC
nonlinear ma
On Jordanian U_{h,\alpha}(gl(2)) Algebra and Its T Matrices Via a Contraction Method
The matrices of the Jordanian U(sl(2)) algebra at
arbitrary dimensions may be obtained from the corresponding
matrices of the standard -deformed U(sl(2)) algebra through a
contraction technique. By extending this method, the coloured two-parametric
() Jordanian matrices of the
U(gl(2)) algebra may be derived from the corresponding coloured
matrices of the standard ()-deformed U(gl(2)) algebra. Moreover, by using the
contraction process as a tool, the coloured matrices for
arbitrary () representations of the Jordanian Fun(GL(2))
algebra may be extracted from the corresponding matrices
of the standard Fun(GL(2)) algebra.Comment: LaTeX, uses amssym.sty, 24 pages, no figure, to be published in Int.
J. Mod. Phys.