On Representations of Conformal Field Theories and the Construction of Orbifolds

We consider representations of meromorphic bosonic chiral conformal field theories, and demonstrate that such a representation is completely specified by a state within the theory. The necessary and sufficient conditions upon this state are derived, and, because of their form, we show that we may extend the representation to a representation of a suitable larger conformal field theory. In particular, we apply this procedure to the lattice (FKS) conformal field theories, and deduce that Dong's proof of the uniqueness of the twisted representation for the reflection-twisted projection of the Leech lattice conformal field theory generalises to an arbitrary even (self-dual) lattice. As a consequence, we see that the reflection-twisted lattice theories of Dolan et al are truly self-dual, extending the analogies with the theories of lattices and codes which were being pursued. Some comments are also made on the general concept of the definition of an orbifold of a conformal field theory in relation to this point of view.Comment: 11 pages, LaTeX. Updated references and added preprint n

Conformal Field Theories, Representations and Lattice Constructions

An account is given of the structure and representations of chiral bosonic meromorphic conformal field theories (CFT's), and, in particular, the conditions under which such a CFT may be extended by a representation to form a new theory. This general approach is illustrated by considering the untwisted and $Z_2$-twisted theories, $H(\Lambda)$ and $\tilde H(\Lambda)$ respectively, which may be constructed from a suitable even Euclidean lattice $\Lambda$. Similarly, one may construct lattices $\Lambda_C$ and $\tilde\Lambda_C$ by analogous constructions from a doubly-even binary code $C$. In the case when $C$ is self-dual, the corresponding lattices are also. Similarly, $H(\Lambda)$ and $\tilde H(\Lambda)$ are self-dual if and only if $\Lambda$ is. We show that $H(\Lambda_C)$ has a natural ``triality'' structure, which induces an isomorphism $H(\tilde\Lambda_C)\equiv\tilde H(\Lambda_C)$ and also a triality structure on $\tilde H(\tilde\Lambda_C)$. For $C$ the Golay code, $\tilde\Lambda_C$ is the Leech lattice, and the triality on $\tilde H(\tilde\Lambda_C)$ is the symmetry which extends the natural action of (an extension of) Conway's group on this theory to the Monster, so setting triality and Frenkel, Lepowsky and Meurman's construction of the natural Monster module in a more general context. The results also serve to shed some light on the classification of self-dual CFT's. We find that of the 48 theories $H(\Lambda)$ and $\tilde H(\Lambda)$ with central charge 24 that there are 39 distinct ones, and further that all 9 coincidences are accounted for by the isomorphism detailed above, induced by the existence of a doubly-even self-dual binary code.Comment: 65 page

The Standard Model Fermion Spectrum From Complex Projective spaces

It is shown that the quarks and leptons of the standard model, including a right-handed neutrino, can be obtained by gauging the holonomy groups of complex projective spaces of complex dimensions two and three. The spectrum emerges as chiral zero modes of the Dirac operator coupled to gauge fields and the demonstration involves an index theorem analysis on a general complex projective space in the presence of topologically non-trivial SU(n)xU(1) gauge fields. The construction may have applications in type IIA string theory and non-commutative geometry.Comment: 13 pages. Typset using LaTeX and JHEP3 style files. Minor typos correcte

Modified Laplace transformation method at finite temperature: application to infra-red problems of N component ϕ4\phi^4 theory

Modified Laplace transformation method is applied to N component $\phi^4$ theory and the finite temperature problem in the massless limit is re-examined in the large N limit. We perform perturbation expansion of the dressed thermal mass in the massive case to several orders and try the massless approximation with the help of modified Laplace transformation. The contribution with fractional power of the coupling constant is recovered from the truncated massive series. The use of inverse Laplace transformation with respect to the mass square is crucial in evaluating the coefficients of fractional power terms.Comment: 16pages, Latex, typographical errors are correcte

TORNADO1 and TORNADO2 are required for the specification of radial and circumferential pattern in the Arabidopsis root

The cell layers of the Arabidopsis primary root are arranged in a simple radial pattern. The outermost layer is the lateral root cap and lies outside the epidermis that surrounds the ground tissue. The files of epidermal and lateral root cap cells converge on a ring of initials (lateral root cap/epidermis initial) from which the epidermal and lateral root cap tissues of the seedling are derived, once root growth is initiated after germination. Each initial gives rise to a clone of epidermal cells and a clone of lateral root cap cells. These initial divisions in the epidermal/lateral root cap initial are defective in tornado1 (trn1) and trn2 plants indicating a requirement for TRN1 and TRN2 for initial cell function. Furthermore, lateral root cap cells develop in the epidermal position in trn1 and trn2 roots indicating that TRN1 and TRN2 are required for the maintenance of the radial pattern of cell specification in the root. The death of these ectopic lateral root cap cells in the elongation zone (where lateral root cap cells normally die) results in the development of gaps in the epidermis. These observations indicate that TRN1 and TRN2 are required to maintain the distinction between the lateral root cap and epidermis and suggest that lateral root cap fate is the default state. It also suggests that TRN1 and TRN2 repress lateral root cap fate in cells in the epidermal location. Furthermore, the position-dependent pattern of root hair and non-root hair cell differentiation in the epidermis is defective in trn1 and trn2 mutants. Together these results indicate that TRN1 and TRN2 are required for the maintenance of both the radial pattern of tissue differentiation in the root and for the subsequent circumferential pattern within the epidermis

SCHIZORIZA controls an asymmetric cell division and restricts epidermal identity in the Arabidopsis root

The primary root of Arabidopsis has a simple cellular organisation. The fixed radial cell pattern results from stereotypical cell divisions that occur in the meristem. Here we describe the characterisation of schizoriza (scz), a mutant with defective radial patterning. In scz mutants, the subepidermal layer (ground tissue) develops root hairs. Root hairs normally only form on epidermal cells of wildtype plants. Moreover, extra periclinal divisions (new wall parallel to surface of the root) occur in the scz root resulting in the formation of supernumerary layers in the ground tissue. Both scarecrow (scr) and short root (shr) suppress the extra periclinal divisions characteristic of scz mutant roots. This results in the formation of a single layered ground tissue in the double mutants. Cells of this layer develop root hairs, indicating that mis-specification of the ground tissue in scz mutants is uncoupled to the cell division defect. This suggests that during the development of the ground tissue SCZ has two distinct roles: (1) it acts as a suppressor of epidermal fate in the ground tissue, and (2) it is required to repress periclinal divisions in the meristem. It may act in the same pathway as SCR and SHR

Physical disruption of intervertebral disc promotes cell clustering and a degenerative phenotype

© 2019, The Author(s). To test the hypothesis that physical disruption of an intervertebral disc disturbs cell-matrix binding, leading to cell clustering and increased expression of matrix degrading enzymes that contribute towards degenerative disc cell phenotype. Lumbar disc tissue was removed at surgery from 21 patients with disc herniation, 11 with disc degeneration, and 8 with adolescent scoliosis. 5 μm sections were examined with histology, and 30-µm sections by confocal microscopy. Antibodies were used against integrin α5beta1, matrix metalloproteinases (MMP) 1, MMP-3, caspase 3, and denatured collagen types I and II. Spatial associations were sought between cell clustering and various degenerative features. An additional, 11 non-herniated human discs were used to examine causality: half of each specimen was cultured in a manner that allowed free ‘unconstrained’ swelling (similar to a herniated disc in vivo), while the other half was cultured within a perspex ring that allowed ‘constrained’ swelling. Changes were monitored over 36 h using live-cell imaging. 1,9-Di-methyl methylene blue (DMMB) assay for glycosaminoglycan loss was carried out from tissue medium. Partially constrained specimens showed little swelling or cell movement in vitro. In contrast, unconstrained swelling significantly increased matrix distortion, glycosaminoglycan loss, exposure of integrin binding sites, expression of MMPs 1 and 3, and collagen denaturation. In the association studies, herniated disc specimens showed changes that resembled unconstrained swelling in vitro. In addition, they exhibited increased cell clustering, apoptosis, MMP expression, and collagen denaturation compared to ‘control’ discs. Results support our hypothesis. Further confirmation will require longitudinal animal experiments

Equivalence between Kaluza Klein modes of gravitinos and goldstinos in brane induced supersymmetry breaking

We identify the goldstino fields that give mass to the Kaluza Klein modes of five dimensional supergravity, when supersymmetry breaking is induced by brane effects. We then proof the four dimensional Equivalence Theorem that, in renormalizable gauges, allows for the replacement of Kaluza Klein modes of helicity $\pm1/2$ gravitinos in terms of goldstinos. Finally we identify the five dimensional renormalizable gauge fixing that leads to the Equivalence Theorem.Comment: Final version published in JHEP. Typo corrected in eq. 2.

Per-protocol investigation of a best practice exercise referral scheme.

Objectives: To investigate the effects of an exercise referral scheme (ERS) aligned to the UK best practice guidelines on a range of outcomes including those associated with key health concerns of the Scottish population. Study design A longitudinal design with data collection at three time points (baseline, midway and post) during a 12-week ERS intervention was employed. Methods: Health-related physical fitness was assessed through measurement of resting heart rate, blood pressure, FEV1:FEV6 (ratio of forced expiratory volume over one [FEV1] and six [FEV6] seconds), body mass and peak oxygen uptake (VO2 peak), whilst functional capacity was assessed through the five times sit to stand test. Psychosocial well-being and quality of life were measured using the World Health Organization Quality of Life questionnaire (WHOQOL-BREF) and the Profile of Mood State questionnaires. Growth curve analyses were used to model each outcome variable across the three time periods. Results: A range of effects were obtained with significant linear improvements in physical performance tests (P < 0.001) and psychosocial assessments (P ≤ 0.002). Additionally, significant quadratic effects of time were obtained for body composition variables and physical activity levels (P < 0.001) with the greatest improvements obtained between baseline and midway assessments. Conclusions: An ERS aligned to the UK best practice guidelines can positively influence a range of health outcomes including those associated with lung function and cardiovascular fitness which are prevalent medical conditions in Scotland. In addition, results indicate that ERS can positively affect outcomes related to functional capacity as well as mental well-being and perceptions of health. The findings of the study identify the need for further investigation including consideration of the initial health status of referred clients