Peter Bowcock

General brane cosmologies and their global spacetime structure

Starting from a completely general standpoint, we find the most general brane-universe solutions for a 3-brane in a five-dimensional spacetime. The brane can border regions of spacetime with or without a cosmological constant. Making no assumptions other than the usual cosmological symmetries of the metric, we prove that the equations of motion form an integrable system, and find the exact solution. The cosmology is indeed a boundary of a (class II) Schwarzschild-AdS spacetime, or a Minkowski (class I) spacetime. We analyse the various cosmological trajectories focusing particularly on those bordering vacuum spacetimes. We find, not surprisingly, that not all cosmologies are compatible with an asymptotically flat spacetime branch. We comment on the role of the radion in this picture.

Classically integrable boundary conditions for affine Toda field theories

Abstract Boundary conditions compatible with classical integrability are studied both directly, using an approach based on the explicit construction of conserved quantities, and indirectly by first developing a generalisation of the Lax pair idea. The latter approach is closer to the spirit of earlier work by Sklyanin and yields a complete set of conjectures for permissible boundary conditions for any affine Toda field theory.

CLASSICALLY INTEGRABLE FIELD THEORIES WITH DEFECTS

Some ideas and remarks are presented concerning a possible Lagrangian approach to the study of internal boundary conditions relating integrable fields at the junction of two domains. The main example given in the article concerns single real scalar fields in each domain and it is found that these may be free, of Liouville type, or of sinh-Gordon type.

On the classification of quantum W-algebras

Abstract In this paper we consider the structure of general quantum W-algebras. We introduce the notions of deformability, positive-definiteness, and reductivity of a W-algebra. We show that one can associate a reductive finite Lie algebra to each reductive W-algebra. The finite Lie algebra is also endowed with a preferred sl(2) subalgebra, which gives the conformal weights of the W-algebra. We extend this to cover W-algebras containing both bosonic and fermionic fields, and illustrate our ideas with the Poisson bracket algebras of generalised Drinfeld-Sokolov hamiltonian systems. We then discuss the possibilities of classifying deformable W-algebras which fall outside this class in the context of automorphisms of Lie algebras. In conclusion we list the cases in which the W-algebra has no weight-one fields, and further, those in which it has only one weight-two field.

Affine Toda field theories with defects

A lagrangian approach is proposed and developed to study defects within affine Toda field theories. In particular, a suitable Lax pair is constructed together with examples of conserved charges. It is found that only those models based on ar(1) data appear to allow defects preserving integrability. Surprisingly, despite the explicit breaking of Lorentz and translation invariance, modified forms of both energy and momentum are conserved. Some, but apparently not all, of the higher spin conserved charges are also preserved after the addition of contributions from the defect. This fact is illustrated by noting how defects may preserve a modified form of just one of the spin 2 or spin -2 charges but not both of them.

Some aspects of jump-defects in the quantum sine-Gordon model

The classical sine-Gordon model permits integrable discontinuities, or jump-defects, where the conditions relating the fields on either side of a defect are Backlund transformations frozen at the defect location. The purpose of this article is to explore the extent to which this idea may be extended to the quantum sine-Gordon model and how the striking features of the classical model may translate to the quantum version. Assuming a positive defect parameter there are two types of defect. One type, carrying even charge, is stable, but the other type, carrying odd charge, is unstable and may be considered as a resonant bound state of a soliton and a stable defect. The scattering of solitons with defects is considered in detail, as is the scattering of breathers, and in all cases the jump-defect is purely transmitting. One surprising discovery concerns the lightest breather. Its transmission factor is independent of the bulk coupling — a property susceptible to a perturbative check, but not shared with any of the other breathers. It is argued that classical jump-defects can move and some comments are made concerning their quantum scattering matrix.

Coset constructions and extended conformal algebras

The structure of coset theories, and the extensions of conformal symmetry which they realise, is considered, using the properties of two special classes of fields, h scalars and v scalars. Series of representations of extended conformal symmetry, associated with cosets of the form gx⊛ hmhm+y, where the subscripts denote the level of the affine algebra, and m runs over the positive integers, are discussed. Those theories possessing a field extending the conformal algebra of weight η, where 1 < η < 2, are listed. The ability of various coset models to be supersymmetrised is established using these techniques. The concept of a dual pair of cosets possessing related partition functions, but not sharing the same extended conformal algebra, is developed.

Exceptional superconformal algebras

Abstract Reductive W-algebras which are generated by bosonic fields of spin 1, a single spin-2 field and fermionic fields of spin - 3 2 are classified. Three new cases are found: a “symplectic” family of superconformal algebras which are extended by su(2)⊗sp(n), an N = 7 and an N = 8 superconformal algebra. The exceptional cases can be viewed as arising a Drinfeld-Sokolov type reduction of the exceptional Lie superalgebras F(4) and G(3), and have an octonionic description. The quantum versions of the superconformal algebras are constructed explicitly in all three cases.

Quasi-primary fields and associativity of chiral algebras

Abstract As a step towards writing down associativity conditions for a general extended conformal algebra, we consider Jacobis identity for a set of quasi-primary fields. In particular, we show that the identity for the subalgebra of operators which generate symmetries of the vacuum can be written in terms of Racah coefficients for su(2). The associativity condition for the full algebra is obtained in an explicit form by considering crossing symmetry of the four-point functions.

Background field boundary conditions for affine Toda field theories

Classical integrability is investigated for affine Toda field theories in the presence of a constant background tensor field. This leads to a further set of discrete possibilities for integrable boundary conditions depending upon the time-derivative of the fields at the boundary but containing no free parameters other than the bulk coupling constant.