Parafermionic Representation of the Affine sl(2/1)sl(2/1) Algebra at Fractional Level

The four fermionic currents of the affine superalgebra $sl(2/1)$ at fractional level $k=1/u-1$, u positive integer, are shown to be realised in terms of a free scalar field, an $sl(2)$ doublet field and a primary field of the parafermionic algebra $Z_{u-1}$.Comment: 5 pages, Latex 2

On a systematic approach to defects in classical integrable field theories

We present an inverse scattering approach to defects in classical integrable field theories. Integrability is proved systematically by constructing the generating function of the infinite set of modified integrals of motion. The contribution of the defect to all orders is explicitely identified in terms of a defect matrix. The underlying geometric picture is that those defects correspond to Backlund transformations localized at a given point. A classification of defect matrices as well as the corresponding defect conditions is performed. The method is applied to a collection of well-known integrable models and previous results are recovered (and extended) directly as special cases. Finally, a brief discussion of the classical $r$-matrix approach in this context shows the relation to inhomogeneous lattice models and the need to resort to lattice regularizations of integrable field theories with defects.Comment: 27 pages, no figures. Final version accepted for publication. References added and section 5 amende

Integrable Field Theories with Defects

The structure of integrable field theories in the presence of defects is discussed in terms of boundary functions under the Lagrangian formalism. Explicit examples of bosonic and fermionic theories are considered. In particular, the boundary functions for the super sinh-Gordon model is constructed and shown to generate the Backlund transformations for its soliton solutions.Comment: talk presented at the XVth International Colloquium on Integrable Systems and Quantum Symmetries, to appear in Czechoslovak Journal of Physics (2006

Characters of admissible representations of the affine superalgebra sl(2|1)

We calculate characters and supercharacters for irreducible, admissible representations of the affine superalgebra sl(2|1) in both the Ramond and Neveu-Schwarz sectors and discuss their modular properties in the special case of level k=-1/2. We also show that the non-degenerate integrable characters coincide with some N=4 superconformal characters

Null vectors, 3-point and 4-point functions in conformal field theory

We consider 3-point and 4-point correlation functions in a conformal field theory with a W-algebra symmetry. Whereas in a theory with only Virasoro symmetry the three point functions of descendants fields are uniquely determined by the three point function of the corresponding primary fields this is not the case for a theory with $W_3$ algebra symmetry. The generic 3-point functions of W-descendant fields have a countable degree of arbitrariness. We find, however, that if one of the fields belongs to a representation with null states that this has implications for the 3-point functions. In particular if one of the representations is doubly-degenerate then the 3-point function is determined up to an overall constant. We extend our analysis to 4-point functions and find that if two of the W-primary fields are doubly degenerate then the intermediate channels are limited to a finite set and that the corresponding chiral blocks are determined up to an overall constant. This corresponds to the existence of a linear differential equation for the chiral blocks with two completely degenerate fields as has been found in the work of Bajnok~et~al.Comment: 10 pages, LaTeX 2.09, DAMTP-93-4

Unconventional cosmology on the (thick) brane

We consider the cosmology of a thick codimension 1 brane. We obtain the matching conditions leading to the cosmological evolution equations and show that when one includes matter with a pressure component along the extra dimension in the brane energy-momentum tensor, the cosmology is of non-standard type. In particular one can get acceleration when a dust of non-relativistic matter particles is the only source for the (modified) Friedman equation. Our equations would seem to violate the conservation of energy-momentum from a 4D perspective, but in 5D the energy-momentum is conserved. One could write down an effective conserved 4D energy-momentum tensor attaching a ``dark energy'' component to the energy-momentum tensor of matter that has pressure along the extra dimension. This extra component could, on a cosmological scale, be interpreted as matter-coupled quintessence. We comment on the effective 4D description of this effect in terms of the time evolution of a scalar field (the 5D radion) coupled to this kind of matter.Comment: 9 pages, v2. eq.(17) corrected, comments on effective theory change

Admissible sl(2/1) Characters and Parafermions

The branching functions of the affine superalgebra $sl(2/1)$ characters into characters of the affine subalgebra $sl(2)$ are calculated for fractional levels $k=1/u-1$, u positive integer. They involve rational torus $A_{u(u-1)}$ and $Z_{u-1}$ parafermion characters.Comment: 14 pages, Latex 2

Affine sl(2|1) and D(2|1;alpha) as Vertex Operator Extensions of Dual Affine sl(2) Algebras

We discover a realisation of the affine Lie superalgebra sl(2|1) and of the exceptional affine superalgebra D(2|1;alpha) as vertex operator extensions of two affine sl(2) algebras with dual levels (and an auxiliary level 1 sl(2) algebra). The duality relation between the levels is (k+1)(k'+1)=1. We construct the representation of sl(2|1) at level k' on a sum of tensor products of sl(2) at level k, sl(2) at level k' and sl(2) at level 1 modules and decompose it into a direct sum over the sl(2|1) spectral flow orbit. This decomposition gives rise to character identities, which we also derive. The extension of the construction to the affine D(2|1;k') at level k is traced to properties of sl(2)+sl(2)+sl(2) embeddings into D(2|1;alpha) and their relation with the dual sl(2) pairs. Conversely, we show how the level k' sl(2) representations are constructed from level k sl(2|1) representations.Comment: 50 pages, Latex2e, 2 figures, acknowledgements adde

Equivalences between spin models induced by defects

The spectrum of integrable spin chains are shown to be independent of the ordering of their spins. As an application we introduce defects (local spin inhomogeneities in homogenous chains) in two-boundary spin systems and, by changing their locations, we show the spectral equivalence of different boundary conditions. In particular we relate certain nondiagonal boundary conditions to diagonal ones.Comment: 14 pages, 16 figures, LaTeX, Extended versio

Physics Opportunities with the FCC-hh Injectors

In this chapter we explore a few examples of physics opportunities using the existing chain of accelerators at CERN, including potential upgrades. In this context the LHC ring is also considered as a part of the injector system. The objective is to find examples that constitute sensitive probes of New Physics that ideally cannot be done elsewhere or can be done significantly better at theCERN accelerator complex. Some of these physics opportunities may require a more flexible injector complex with additional functionality than that just needed to inject protons into the FCC-hh at the right energy, intensity and bunch structure. Therefore it is timely to discuss these options concurrently with the conceptual design of the FCC-hh injector system.Comment: 13 pages, chapter 5 in Physics at the FCC-hh, a 100 TeV pp collide