4 research outputs found
On the Cohomology of the Noncritical -string
We investigate the cohomology structure of a general noncritical
-string. We do this by introducing a new basis in the Hilbert space in
which the BRST operator splits into a ``nested'' sum of nilpotent BRST
operators. We give explicit details for the case . In that case the BRST
operator can be written as the sum of two, mutually anticommuting,
nilpotent BRST operators: . We argue that if one chooses for the
Liouville sector a minimal model then the cohomology of the
operator is closely related to a Virasoro minimal model. In particular,
the special case of a (4,3) unitary minimal model with central charge
leads to a Ising model in the cohomology. Despite all this,
noncritical strings are not identical to noncritical Virasoro strings.Comment: 38 pages, UG-7/93, ITP-SB-93-7
A BRST Analysis of -symmetries
We perform a classical BRST analysis of the symmetries corresponding to a
generic -algebra. An essential feature of our method is that we write the
-algebra in a special basis such that the algebra manifestly has a
``nested'' set of subalgebras where the subalgebra consists of
generators of spin , respectively. In the new basis the
BRST charge can be written as a ``nested'' sum of nilpotent BRST charges.
In view of potential applications to (critical and/or non-critical) -string
theories we discuss the quantum extension of our results. In particular, we
present the quantum BRST-operator for the -algebra in the new basis. For
both critical and non-critical -strings we apply our results to discuss the
relation with minimal models.Comment: 32 pages, UG-4/9
W-Gravity
The geometric structure of theories with gauge fields of spins two and higher
should involve a higher spin generalisation of Riemannian geometry. Such
geometries are discussed and the case of -gravity is analysed in
detail. While the gauge group for gravity in dimensions is the
diffeomorphism group of the space-time, the gauge group for a certain
-gravity theory (which is -gravity in the case ) is the group
of symplectic diffeomorphisms of the cotangent bundle of the space-time. Gauge
transformations for -gravity gauge fields are given by requiring the
invariance of a generalised line element. Densities exist and can be
constructed from the line element (generalising )
only if or , so that only for can actions be constructed.
These two cases and the corresponding -gravity actions are considered in
detail. In , the gauge group is effectively only a subgroup of the
symplectic diffeomorphism group. Some of the constraints that arise for
are similar to equations arising in the study of self-dual four-dimensional
geometries and can be analysed using twistor methods, allowing contact to be
made with other formulations of -gravity. While the twistor transform for
self-dual spaces with one Killing vector reduces to a Legendre transform, that
for two Killing vectors gives a generalisation of the Legendre transform.Comment: 49 pages, QMW-92-