87 research outputs found
Hyperbolic Kac-Moody superalgebras
We present a classification of the hyperbolic Kac-Moody (HKM) superalgebras.
The HKM superalgebras of rank larger or equal than 3 are finite in number (213)
and limited in rank (6). The Dynkin-Kac diagrams and the corresponding simple
root systems are determined. We also discuss a class of singular
sub(super)algebras obtained by a folding procedure
Yukawa terms in noncommutative SO(10) and E6 GUTs
We propose a method for constructing Yukawa terms for noncommutative SO(10)
and E6 GUTs, when these GUTs are formulated within the enveloping-algebra
formalism. The most general noncommutative Yukawa term that we propose
contains, at first order in thetamunu, the most general BRS invariant Yukawa
contribution whose only dimensionful parameter is the noncommutativity
parameter. This noncommutative Yukawa interaction is thus renormalisable at
first order in thetamunu.Comment: 14 pages, no figure
Anyonic Realization of the Quantum Affine Lie Superalgebra U_q(A(M,N)^{(1)})
We give a realization of the quantum affine Lie superalgebras U_q(A(M,N))^(1)
in terms of anyons defined on a one or two-dimensional lattice, the deformation
parameter q being related to the statistical parameter of the anyons by q
= exp(i\pi\nu). The construction uses anyons contructed from usual fermionic
oscillators and deformed bosonic oscillators. As a byproduct, realization
deformed in any sector of the quantum superalgebras U_q(A(M,N)) is obtained.Comment: 14p LaTeX Document (should be run twice
Orthosymplectically invariant functions in superspace
The notion of spherically symmetric superfunctions as functions invariant
under the orthosymplectic group is introduced. This leads to dimensional
reduction theorems for differentiation and integration in superspace. These
spherically symmetric functions can be used to solve orthosymplectically
invariant Schroedinger equations in superspace, such as the (an)harmonic
oscillator or the Kepler problem. Finally the obtained machinery is used to
prove the Funk-Hecke theorem and Bochner's relations in superspace.Comment: J. Math. Phy
Quantum Loop Subalgebra and Eigenvectors of the Superintegrable Chiral Potts Transfer Matrices
It has been shown in earlier works that for Q=0 and L a multiple of N, the
ground state sector eigenspace of the superintegrable tau_2(t_q) model is
highly degenerate and is generated by a quantum loop algebra L(sl_2).
Furthermore, this loop algebra can be decomposed into r=(N-1)L/N simple sl_2
algebras. For Q not equal 0, we shall show here that the corresponding
eigenspace of tau_2(t_q) is still highly degenerate, but splits into two
spaces, each containing 2^{r-1} independent eigenvectors. The generators for
the sl_2 subalgebras, and also for the quantum loop subalgebra, are given
generalizing those in the Q=0 case. However, the Serre relations for the
generators of the loop subalgebra are only proven for some states, tested on
small systems and conjectured otherwise. Assuming their validity we construct
the eigenvectors of the Q not equal 0 ground state sectors for the transfer
matrix of the superintegrable chiral Potts model.Comment: LaTeX 2E document, using iopart.cls with iopams packages. 28 pages,
uses eufb10 and eurm10 fonts. Typeset twice! Version 2: Details added,
improvements and minor corrections made, erratum to paper 2 included. Version
3: Small paragraph added in introductio
Development of a unified tensor calculus for the exceptional Lie algebras
The uniformity of the decomposition law, for a family F of Lie algebras which
includes the exceptional Lie algebras, of the tensor powers ad^n of their
adjoint representations ad is now well-known. This paper uses it to embark on
the development of a unified tensor calculus for the exceptional Lie algebras.
It deals explicitly with all the tensors that arise at the n=2 stage, obtaining
a large body of systematic information about their properties and identities
satisfied by them. Some results at the n=3 level are obtained, including a
simple derivation of the the dimension and Casimir eigenvalue data for all the
constituents of ad^3. This is vital input data for treating the set of all
tensors that enter the picture at the n=3 level, following a path already known
to be viable for a_1. The special way in which the Lie algebra d_4 conforms to
its place in the family F alongside the exceptional Lie algebras is described.Comment: 27 pages, LaTeX 2
Knots in Chern-Simons Field Theory
Knots in the Chern-Simons field theory with Lie super gauge group
are studied, and the polynomial invariant with skein relations are obtained under the fundamental
representation of .Comment: 15 pages, 5 figure
Conserved Charges in the Principal Chiral Model on a Supergroup
The classical principal chiral model in 1+1 dimensions with target space a
compact Lie supergroup is investigated. It is shown how to construct a local
conserved charge given an invariant tensor of the Lie superalgebra. We
calculate the super-Poisson brackets of these currents and argue that they are
finitely generated. We show how to derive an infinite number of local charges
in involution. We demonstrate that these charges Poisson commute with the
non-local charges of the model
Classical Lie algebras and Drinfeld doubles
The Drinfeld double structure underlying the Cartan series An, Bn, Cn, Dn of
simple Lie algebras is discussed.
This structure is determined by two disjoint solvable subalgebras matched by
a pairing. For the two nilpotent positive and negative root subalgebras the
pairing is natural and in the Cartan subalgebra is defined with the help of a
central extension of the algebra.
A new completely determined basis is found from the compatibility conditions
in the double and a different perspective for quantization is presented. Other
related Drinfeld doubles on C are also considered.Comment: 11 pages. submitted for publication to J. Physics
Strings from Gauged Wess-Zumino-Witten Models
We present an algebraic approach to string theory. An embedding of
in a super Lie algebra together with a grading on the Lie algebra determines a
nilpotent subalgebra of the super Lie algebra. Chirally gauging this subalgebra
in the corresponding Wess-Zumino-Witten model, breaks the affine symmetry of
the Wess-Zumino-Witten model to some extension of the superconformal
algebra. The extension is completely determined by the embedding. The
realization of the superconformal algebra is determined by the grading. For a
particular choice of grading, one obtains in this way, after twisting, the BRST
structure of a string theory. We classify all embeddings of into Lie
super algebras and give a detailed account of the branching of the adjoint
representation. This provides an exhaustive classification and characterization
of both all extended superconformal algebras and all string theories
which can be obtained in this way.Comment: 50 pages, LaTe
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