Tree scattering amplitudes of the spin-4/3 fractional superstring I: the untwisted sectors

Scattering amplitudes of the spin-4/3 fractional superstring are shown to satisfy spurious state decoupling and cyclic symmetry (duality) at tree-level in the string perturbation expansion. This fractional superstring is characterized by the spin-4/3 fractional superconformal algebra---a parafermionic algebra studied by Zamolodchikov and Fateev involving chiral spin-4/3 currents on the world-sheet in addition to the stress-energy tensor. Examples of tree scattering amplitudes are calculated in an explicit c=5 representation of this fractional superconformal algebra realized in terms of free bosons on the string world-sheet. The target space of this model is three-dimensional flat Minkowski space-time with a level-2 Kac-Moody so(2,1) internal symmetry, and has bosons and fermions in its spectrum. Its closed string version contains a graviton in its spectrum. Tree-level unitarity (i.e., the no-ghost theorem for space-time bosonic physical states) can be shown for this model. Since the critical central charge of the spin-4/3 fractional superstring theory is 10, this c=5 representation cannot be consistent at the string loop level. The existence of a critical fractional superstring containing a four-dimensional space-time remains an open question.Comment: 42 pages, 4 figures, latex, IASSNS-HEP-93/57, CLNS-92/117

Kac and New Determinants for Fractional Superconformal Algebras

We derive the Kac and new determinant formulae for an arbitrary (integer) level $K$ fractional superconformal algebra using the BRST cohomology techniques developed in conformal field theory. In particular, we reproduce the Kac determinants for the Virasoro ($K=1$) and superconformal ($K=2$) algebras. For $K\geq3$ there always exist modules where the Kac determinant factorizes into a product of more fundamental new determinants. Using our results for general $K$, we sketch the non-unitarity proof for the $SU(2)$ minimal series; as expected, the only unitary models are those already known from the coset construction. We apply the Kac determinant formulae for the spin-4/3 parafermion current algebra ({\em i.e.}, the $K=4$ fractional superconformal algebra) to the recently constructed three-dimensional flat Minkowski space-time representation of the spin-4/3 fractional superstring. We prove the no-ghost theorem for the space-time bosonic sector of this theory; that is, its physical spectrum is free of negative-norm states.Comment: 33 pages, Revtex 3.0, Cornell preprint CLNS 93/124

New Jacobi-Like Identities for Z_k Parafermion Characters

We state and prove various new identities involving the Z_K parafermion characters (or level-K string functions) for the cases K=4, K=8, and K=16. These identities fall into three classes: identities in the first class are generalizations of the famous Jacobi theta-function identity (which is the K=2 special case), identities in another class relate the level K>2 characters to the Dedekind eta-function, and identities in a third class relate the K>2 characters to the Jacobi theta-functions. These identities play a crucial role in the interpretation of fractional superstring spectra by indicating spacetime supersymmetry and aiding in the identification of the spacetime spin and statistics of fractional superstring states.Comment: 72 pages (or 78/2 = 39 pages in reduced format

Low-Lying States of the Six-Dimensional Fractional Superstring

The $K=4$ fractional superstring Fock space is constructed in terms of \bZ_4 parafermions and free bosons. The bosonization of the \bZ_4 parafermion theory and the generalized commutation relations satisfied by the modes of various parafermion fields are reviewed. In this preliminary analysis, we describe a Fock space which is simply a tensor product of \bZ_4 parafermion and free boson Fock spaces. It is larger than the Lorentz-covariant Fock space indicated by the fractional superstring partition function. We derive the form of the fractional superconformal algebra that may be used as the constraint algebra for the physical states of the FSS. Issues concerning the associativity, modings and braiding properties of the fractional superconformal algebra are also discussed. The use of the constraint algebra to obtain physical state conditions on the spectrum is illustrated by an application to the massless fermions and bosons of the $K=4$ fractional superstring. However, we fail to generalize these considerations to the massive states. This means that the appropriate constraint algebra on the fractional superstring Fock space remains to be found. Some possible ways of doing this are discussed.Comment: 69 pages, LaTeX, CLNS 91/112

A note on spin-s duality

Duality is investigated for higher spin ($s \geq 2$), free, massless, bosonic gauge fields. We show how the dual formulations can be derived from a common "parent", first-order action. This goes beyond most of the previous treatments where higher-spin duality was investigated at the level of the equations of motion only. In D=4 spacetime dimensions, the dual theories turn out to be described by the same Pauli-Fierz (s=2) or Fronsdal ($s \geq 3$) action (as it is the case for spin 1). In the particular s=2 D=5 case, the Pauli-Fierz action and the Curtright action are shown to be related through duality. A crucial ingredient of the analysis is given by the first-order, gauge-like, reformulation of higher spin theories due to Vasiliev.Comment: Minor corrections, reference adde

Hyperbolic billiards of pure D=4 supergravities

We compute the billiards that emerge in the Belinskii-Khalatnikov-Lifshitz (BKL) limit for all pure supergravities in D=4 spacetime dimensions, as well as for D=4, N=4 supergravities coupled to k (N=4) Maxwell supermultiplets. We find that just as for the cases N=0 and N=8 investigated previously, these billiards can be identified with the fundamental Weyl chambers of hyperbolic Kac-Moody algebras. Hence, the dynamics is chaotic in the BKL limit. A new feature arises, however, which is that the relevant Kac-Moody algebra can be the Lorentzian extension of a twisted affine Kac-Moody algebra, while the N=0 and N=8 cases are untwisted. This occurs for N=5, N=3 and N=2. An understanding of this property is provided by showing that the data relevant for determining the billiards are the restricted root system and the maximal split subalgebra of the finite-dimensional real symmetry algebra characterizing the toroidal reduction to D=3 spacetime dimensions. To summarize: split symmetry controls chaos.Comment: 21 page

Kac-Moody algebras in perturbative string theory

The conjecture that M-theory has the rank eleven Kac-Moody symmetry e11 implies that Type IIA and Type IIB string theories in ten dimensions possess certain infinite dimensional perturbative symmetry algebras that we determine. This prediction is compared with the symmetry algebras that can be constructed in perturbative string theory, using the closed string analogues of the DDF operators. Within the limitations of this construction close agreement is found. We also perform the analogous analysis for the case of the closed bosonic string.Comment: 31 pages, harvmac (b), 4 eps-figure

Superconformal Selfdual Sigma-Models

A range of bosonic models can be expressed as (sometimes generalized) $\sigma$-models, with equations of motion coming from a selfduality constraint. We show that in D=2, this is easily extended to supersymmetric cases, in a superspace approach. In particular, we find that the configurations of fields of a superconformal $\mathfrak{G}/\mathfrak{H}$ coset models which satisfy some selfduality constraint are automatically solutions to the equations of motion of the model. Finally, we show that symmetric space $\sigma$-models can be seen as infinite-dimensional \tfG/\tfH models constrained by a selfduality equation, with \tfG the loop extension of $\mathfrak{G}$ and \tfH a maximal subgroup. It ensures that these models have a hidden global \tfG symmetry together with a local \tfH gauge symmetry.Comment: 21 pages; v2 few corrections and references added; v3 exposition change

Differences in biopsychosocial profiles of diabetes patients by level of glycaemic control and health-related quality of life: The Maastricht Study

Aims Tailored, patient-centred innovations are needed in the care for persons with type 2 diabetes mellitus (T2DM), in particular those with insufficient glycaemic control. Therefore, this study sought to assess their biopsychosocial characteristics and explore whether distinct biopsychosocial profiles exist within this subpopulation, which differ in health-related quality of life (HRQoL). Methods Cross-sectional study based on data from The Maastricht Study, a population-based cohort study focused on the aetiology, pathophysiology, complications, and comorbidities of T2DM. We analysed associations and clustering of glycaemic control and HRQoL with 38 independent variables (i.e. biopsychosocial characteristics) in different subgroups and using descriptive analyses, latent class analysis (LCA), and logistic regressions. Results Included were 840 persons with T2DM, mostly men (68.6%) and with a mean age of 62.6 (±7.7) years. Mean HbA1c was 7.1% (±3.2%); 308 patients (36.7%) had insufficient glycaemic control (HbA1c>7.0% [53 mmol/mol]). Compared to those with sufficient control, these patients had a significantly worse-off status on multiple biopsychosocial factors, including self-efficacy, income, education and several health-related characteristics. Two ‘latent classes’ were identified in the insufficient glycaemic control subgroup: with low respectively high HRQoL. Of the two, the low HRQoL class comprised about one-fourth of patients and had a significantly worse biopsychosocial profile. Conclusions Insufficient glycaemic control, particularly in combination with low HRQoL, is associated with a generally worse biopsychosocial profile. Further research is needed into the complex and multidimensional causal pathways explored in this study, so as to increase our understanding of the heterogeneous care needs and preferences of persons with T2DM, and translate this knowledge into tailored care and support arrangements