164 research outputs found
The -string spectrum
We study the spectrum of strings. In particular, we show that for
appropriately chosen space-time signature, one of the scalar fields is singled
out by the spin-3 constraint and is ``frozen'': no creation operators from it
can appear in physical states and the corresponding momentum must assume a
specific fixed value. The remaining theory is unitary and resembles an ordinary
string theory in with anomalies cancelled by appropriate background
charges. In the case of the string, however, the spin-two ``graviton'' is
massive.Comment: 14 Page
Generalised Holonomy for Higher-Order Corrections to Supersymmetric Backgrounds in String and M-Theory
The notion of {\it generalised structure groups} and {\it generalised
holonomy groups} has been introduced in supergravity, in order to discuss the
spinor rotations generated by commutators of supercovariant derivatives when
non-vanishing form fields are included, with their associated gamma-matrix
structures that go beyond the usual \Gamma_{MN} of the Riemannian connection.
In this paper we investigate the generalisations to the usual Riemannian
structure and holonomy groups that result from the inclusion of higher-order
string or M-theory corrections in the supercovariant derivative. Even in the
absence of background form fields, these corrections introduce additional terms
\Gamma_{M_1... M_6} in the supercovariant connection, and hence they lead to
enlarged structure and holonomy groups. In some cases, the corrected equations
of motion force form fields to become non-zero too, which can further enlarge
the groups. Our investigation focuses on the generalised structure and holonomy
groups in the transverse spaces K_n of (Minkowski) \times K_n backgrounds for
n=6, 7, 8 and 10, and shows how the generalised holonomies allow the continued
existence of supersymmetric backgrounds even though the usual Riemannian
special holonomy is destroyed by the inclusion of the string or M-theory
corrections.Comment: Latex, 23 pages, clarifying comments and references adde
Weyl Group Invariance and p-brane Multiplets
In this paper, we study the actions of the Weyl groups of the U duality
groups for type IIA string theory toroidally compactified to all dimensions
. We show how these Weyl groups implement permutations of the field
strengths, and we discuss the Weyl group multiplets of all supersymmetric
-brane solitons.Comment: 31 pages, Late
Canonical BRST Quantisation of Worldsheet Gravities
We reformulate the BRST quantisation of chiral Virasoro and worldsheet
gravities. Our approach follows directly the classic BRST formulation of
Yang-Mills theory in employing a derivative gauge condition instead of the
conventional conformal gauge condition, supplemented by an introduction of
momenta in order to put the ghost action back into first-order form. The
consequence of these simple changes is a considerable simplification of the
BRST formulation, the evaluation of anomalies and the expression of Wess-Zumino
consistency conditions. In particular, the transformation rules of all fields
now constitute a canonical transformation generated by the BRST operator ,
and we obtain in this reformulation a new result that the anomaly in the BRST
Ward identity is obtained by application of the anomalous operator ,
calculated using operator products, to the gauge fermion.Comment: 27 pages. (Some factors of \hbar corrected
Embedding of the Bosonic String into the String
We investigate new realisations of the algebra with arbitrary central
charge, making use of the fact that this algebra can be linearised by the
inclusion of a spin-1 current. We use the new realisations with and
to build non-critical and critical BRST operators. Both of these
can be converted by local canonical transformations into a BRST operator for
the Virasoro string with , together with a Kugo-Ojima topological term.
Consequently, these new realisations provide embeddings of the Virasoro string
into non-critical and critical strings.Comment: 11 pages. (Some referencing changes
Higher-Order Corrections to Non-Compact Calabi-Yau Manifolds in String Theory
At the leading order, the low-energy effective field equations in string
theory admit solutions of the form of products of Minkowski spacetime and a
Ricci-flat Calabi-Yau space. The equations of motion receive corrections at
higher orders in \alpha', which imply that the Ricci-flat Calabi-Yau space is
modified. In an appropriate choice of scheme, the Calabi-Yau space remains
Kahler, but is no longer Ricci-flat. We discuss the nature of these corrections
at order {\alpha'}^3, and consider the deformations of all the known
cohomogeneity one non-compact Kahler metrics in six and eight dimensions. We do
this by deriving the first-order equations associated with the modified
Killing-spinor conditions, and we thereby obtain the modified supersymmetric
solutions. We also give a detailed discussion of the boundary terms for the
Euler complex in six and eight dimensions, and apply the results to all the
cohomogeneity one examples.Comment: Latex, 49 pages. References added, typos corrected, and discussion
and conclusions extende
Vertical versus Diagonal Dimensional Reduction for p-branes
In addition to the double-dimensional reduction procedure that employs
world-volume Killing symmetries of -brane supergravity solutions and acts
diagonally on a plot of versus spacetime dimension , there exists a
second procedure of ``vertical'' reduction. This reduces the transverse-space
dimension via an integral that superposes solutions to the underlying Laplace
equation. We show that vertical reduction is also closely related to the
recently-introduced notion of intersecting -branes. We illustrate this with
examples, and also construct a new solution describing four intersecting
membranes, which preserves of the supersymmetry. Given the two reduction
schemes plus duality transformations at special points of the scalar modulus
space, one may relate most of the -brane solutions of relevance to
superstring theory. We argue that the maximum classifying duality symmetry for
this purpose is the Weyl group of the corresponding Cremmer-Julia supergravity
symmetry . We also discuss a separate class of duality-invariant
-branes with .Comment: Latex, 21 pages, no figures. References adde
Linearly-realised Worldsheet Supersymmetry in pp-wave Background
We study the linearly-realised worldsheet supersymmetries in the ``massive''
type II light-cone actions for pp-wave backgrounds. The pp-waves have have
16+N_sup Killing spinors, comprising 16 ``standard'' Killing spinors that occur
in any wave background, plus N_sup ``supernumerary'' Killing spinors (0\le
N_sup \le 16) that occur only for special backgrounds. We show that only the
supernumerary Killing spinors give rise to linearly-realised worldsheet
supersymmetries after light-cone gauge fixing, while the 16 standard Killing
spinors describe only non-linearly realised inhomogeneous symmetries. We also
study the type II actions in the physical gauge, and we show that although in
this case the actions are not free, there are now linearly-realised
supersymmetries coming both from the standard and the supernumerary Killing
spinors. In the physical gauge, there are no mass terms for any worldsheet
degrees of freedom, so the masses appearing in the light-cone gauge may be
viewed as gauge artefacts. We obtain type IIA and IIB supergravity solutions
describing solitonic strings in pp-wave backgrounds, and show how these are
related to the physical-gauge fundamental string actions. We study the
supersymmetries of these solutions, and find examples with various numbers of
Killing spinors, including total numbers that are odd.Comment: Latex, 35 page
The Multivalued Free-Field Maps of Liouville and Toda Gravities
Liouville and Toda gravity theories with non-vanishing interaction potentials
have spectra obtained by dividing the free-field spectra for these cases by the
Weyl group of the corresponding or Lie algebra. We study the
canonical transformations between interacting and free fields using the
technique of intertwining operators, giving explicit constructions for the
wavefunctions and showing that they are invariant under the corresponding Weyl
groups. These explicit constructions also permit a detailed analysis of the
operator-state maps and of the nature of the Seiberg bounds.Comment: 47 pages, plain Tex, 5 Postscript figures, uses epsf.tex. Repackaging
to permit Postscript generation, no changes to pape
Superdualities, brane tensions and massive IIA/IIB duality
The gauge transformations of p-form fields in supergravity theories acquire a
non-commuting character when one introduces potentials both for the theory's
original field strengths and for their duals. This has previously been shown in
the ``doubled'' formalism for maximal supergravities, where a generalised
duality relation between original and dual field strengths replaces the
equations of motion. In the doubled formalism, the gauge transformations
generate a superalgebra, and the corresponding symmetries have accordingly been
called ``superdualities.'' The corresponding Noether charges form a
representation of the cohomology ring on the spacetime manifold. In this paper,
we show that the gauge symmetry superalgebra implies certain non-trivial
relations among the various p-brane tensions, which can straightforwardly be
read off from the superalgebra commutation relations. This provides an elegant
derivation of the brane-tension relations purely within a given theory, without
the need to make use of duality relations between different theories, such as
the type IIA/IIB T-duality, although the results are consistent with such
dualities. We present the complete set of brane-tension relations in M-theory,
in the type IIA and type IIB theories, and in all the lower-dimensional maximal
supergravities. We also construct a doubled formalism for massive type IIA
supergravity, and this enables us to obtain the brane-tension relations
involving the D8-brane, purely within the framework of the massive IIA theory.
We also obtain explicit transformations for the nine-dimensional T-duality
between the massive type IIA theory and the Scherk-Schwarz reduced type IIB
theory.Comment: LaTeX, 30 pages, references adde
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