221 research outputs found
Higher-spin strings and W minimal models
We study the spectrum of physical states for higher-spin generalisations of
string theory, based on two-dimensional theories with local spin-2 and spin-
symmetries. We explore the relation of the resulting effective Virasoro string
theories to certain minimal models. In particular, we show how the
highest-weight states of the minimal models decompose into Virasoro
primaries.Comment: 13 pages, CTP TAMU-43/93, KUL-TF-93/9
Quantising Higher-spin String Theories
In this paper, we examine the conditions under which a higher-spin string
theory can be quantised. The quantisability is crucially dependent on the way
in which the matter currents are realised at the classical level. In
particular, we construct classical realisations for the algebra,
which is generated by a primary spin- current in addition to the
energy-momentum tensor, and discuss the quantisation for . From these
examples we see that quantum BRST operators can exist even when there is no
quantum generalisation of the classical algebra. Moreover, we find
that there can be several inequivalent ways of quantising a given classical
theory, leading to different BRST operators with inequivalent cohomologies. We
discuss their relation to certain minimal models. We also consider the
hierarchical embeddings of string theories proposed recently by Berkovits and
Vafa, and show how the already-known strings provide examples of this
phenomenon. Attempts to find higher-spin fermionic generalisations lead us to
examine the whether classical BRST operators for ( odd)
algebras can exist. We find that even though such fermionic algebras close up
to null fields, one cannot build nilpotent BRST operators, at least of the
standard form.Comment: CTP TAMU-24/94, KUL-TF-94/11, SISSA-135/94/E
A note on W_{2,s} strings
BRST operators for two-dimensional theories with spin-2 and spin-
currents, generalising the BRST operator of Thierry-Mieg, have previously
been obtained. The construction was based on demanding nilpotence of the BRST
operators, making no reference to whether or not an underlying algebra
exists. In this paper, we analyse the known cases (, 4, 5 and 6), showing
that the two BRST operators are associated with the algebra, and
that two of the four BRST operators are associated with the
algebra. We discuss the cohomology of all the known higher-spin BRST operators,
the Weyl symmetry of their physical states, and their relation with certain
minimal models. We also obtain the BRST operator for the case .Comment: 12 pages, CTP TAMU-8/94, LZU-TH-94/0
On the symmetries of special holonomy sigma models
In addition to superconformal symmetry, (1,1) supersymmetric two-dimensional
sigma models on special holonomy manifolds have extra symmetries that are in
one-to-one correspondence with the covariantly constant forms on these
manifolds. The superconformal algebras extended by these symmetries close as
W-algebras, i.e. they have field-dependent structure functions. It is shown
that it is not possible to write down cohomological equations for potential
quantum anomalies when the structure functions are field-dependent. In order to
do this it is necessary to linearise the algebras by treating composite
currents as generators of additional symmetries. It is shown that all cases can
be linearised in a finite number of steps, except for G_2 and SU(3). Additional
problems in the quantisation procedure are briefly discussed.Comment: 16 pages. Abstract improved and a few typographical errors correcte
Anomaly Freedom and Realisations for Super- Strings
We construct new multi-field realisations of the super- algebra,
which are important for building super- string theories. We derive the
structure of the ghost vacuum for such theories, and use the result to
calculate the intercepts. These results determine the conditions for physical
states in the super- string theory.Comment: 22 page
The Complete Spectrum of the String
We obtain the complete physical spectrum of the string, for arbitrary
. The constraints freeze coordinates, while the remaining
coordinates appear in the currents only {\it via} their energy-momentum tensor.
The spectrum is then effectively described by a set of ordinary Virasoro-like
string theories, but with a non-critical value for the central charge and a
discrete set of non-standard values for the spin-2 intercepts. In particular,
the physical spectrum of the string includes the usual massless states of
the Virasoro string. By looking at the norms of low-lying states, we find
strong indications that all the strings are unitary.Comment: 28 page
The Interacting String
We present a procedure for computing gauge-invariant scattering amplitudes in
the string, and use it to calculate three-point and four-point functions.
We show that non-vanishing scattering amplitudes necessarily involve external
physical states with excitations of ghosts as well as matter fields. The
crossing properties of the four-point functions are studied, and it is shown
that the duality of the Virasoro string amplitudes generalises in the
string, with different sets of intermediate states being exchanged in different
channels. We also exhibit a relation between the scattering amplitudes of the
string and the fusion rules of the Ising model.Comment: (Revised version), 26 pages, Plain Tex, CTP TAMU-86/92, KUL-TF-92/4
Division Algebras and Extended N=2,4,8 SuperKdVs
The first example of an N=8 supersymmetric extension of the KdV equation is
here explicitly constructed. It involves 8 bosonic and 8 fermionic fields. It
corresponds to the unique N=8 solution based on a generalized hamiltonian
dynamics with (generalized) Poisson brackets given by the Non-associative N=8
Superconformal Algebra. The complete list of inequivalent classes of
parametric-dependent N=3 and N=4 superKdVs obtained from the ``Non-associative
N=8 SCA" is also furnished. Furthermore, a fundamental domain characterizing
the class of inequivalent N=4 superKdVs based on the "minimal N=4 SCA" is
given.Comment: 14 pages, LaTe
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