50 research outputs found
Fractional Supersymmetry
A Symmetry between bosonic coordinates and some Grassmannian-type coordinates
is presented. Commuting two of these Grassmannian-type variables results in an
arbitrary phase (not just a minus sign). This symmetry is also realised at the
level of the field theory.Comment: 5 pages, Late
Gauss Decomposition, Wakimoto Realisation and Gauged WZNW Models
The implications of gauging the Wess-Zumino-Novikov-Witten (WZNW) model using
the Gauss decomposition of the group elements are explored. We show that,
contrary to standard gauging of WZNW models, this gauging is carried out by
minimally coupling the gauge fields. We find that this gauging, in the case of
gauging an abelian vector subgroup, differs from the standard one by terms
proportional to the field strength of the gauge fields. We prove that gauging
an abelian vector subgroup does not have a nonlinear sigma model
interpretation. This is because the target-space metric resulting from the
integration over the gauge fields is degenerate. We demonstrate, however, that
this kind of gauging has a natural interpretation in terms of Wakimoto
variables.Comment: 17 pages, BONN-HE-93-4
N=2 Current Algebras for Non-Semi-Simple Groups
We examine the problem of constructing N=2 superconformal algebras out of N=1
non-semi-simple affine Lie algebras. These N=2 superconformal theories share
the property that the super Virasoro central charge depends only on the
dimension of the Lie algebra. We find, in particular, a construction having a
central charge c=9. This provides a possible internal space for string
compactification and where mirror symmetry might be explored.Comment: 10 pages, BONN-HE-94-0
A Novel Symmetry in Sigma Models
A class of non-linear sigma models possessing a new symmetry is identified.
The same symmetry is also present in Chern-Simons theories. This hints at a
possible topological origin for this class of sigma models. The non-linear
sigma models obtained by non-Abelian duality are a particular case in this
class.Comment: 9 pages, latex, no figure
Wess-Zumino-Novikov-Witten Models Based on Lie Superalgebras
The affine current algebra for Lie superalgebras is examined. The bilinear
invariant forms of the Lie superalgebra can be either degenerate or
non-degenerate. We give the conditions for a Virasoro construction, in which
the currents are primary fields of weight one, to exist. In certain cases, the
Virasoro central charge is an integer equal to the super dimension of the group
supermanifold. A Wess-Zumino-Novikov-Witten action based on these Lie
superalgebras is also found.Comment: 10 pages, Latexfile, BONN-TH-94-0
Anti-field Formalism and Non-Abelian Duality
The act of implementing non-Abelian duality in two dimensional sigma models
results unavoidably in an additional reducible symmetry. The Batalin-Vilkovisky
formalism is employed to handle this new symmetry. Valuable lessons are learnt
here with respect to non-Abelian duality. We emphasise, in particular, the
effects of the ghost sector corresponding to this symmetry on non-Abelian
duality.Comment: 13 pages, LaTeX2
Non-Abelian Duality Based on Non-Semi-Simple Isometry Groups
Non-Abelian duality transformations built on non-semi-simple isometry groups
are analysed. We first give the conditions under which the original non-linear
sigma model and its non-Abelian dual are equivalent. The existence of an
invariant and non-degenerate bilinear form for the isometry Lie algebra is
crucial for this equivalence. The non-Abelian dual of a conformally invariant
sigma model, with non-semi-simple isometries, is then constructed and its beta
functions are shown to vanish. This study resolves an apparent obstruction to
the conformal invariance of sigma models obtained via non-Abelian duality based
on non-semi-simple groups.Comment: 13 pages, Latex file, to appear in Phys. Lett.