Conformal Partial Waves and the Operator Product Expansion

By solving the two variable differential equations which arise from finding the eigenfunctions for the Casimir operator for $O(d,2)$ succinct expressions are found for the functions, conformal partial waves, representing the contribution of an operator of arbitrary scale dimension $\Delta$ and spin $\ell$ together with its descendants to conformal four point functions for $d=4$, recovering old results, and also for $d=6$. The results are expressed in terms of ordinary hypergeometric functions of variables $x,z$ which are simply related to the usual conformal invariants. An expression for the conformal partial wave amplitude valid for any dimension is also found in terms of a sum over two variable symmetric Jack polynomials which is used to derive relations for the conformal partial waves.Comment: 17 pages, uses harvmac, v2 correction to eq. 2.2

Dualities in Supersymmetric Field Theories

Lectures presented at the 33rd Karpacz Winter School ``Duality: Strings and Fields'' briefly introducing dualities in four-dimensional quantum field theory, and summarizing results found in supersymmetric field theories. The first lecture describes physical aspects of electric-magnetic (EM), strong-weak coupling (S), and infrared (IR) dualities. The second lecture focuses on results and conjectures concerning S-duality in N=2 supersymmetric gauge theories. The third lecture discusses IR-dualities and their relation to S-duality in N=1 supersymmetric field theories.Comment: 9 pages, latex with espcrc2.st

Old and new results for superenergy tensors from dimensionally dependent tensor identities

It is known that some results for spinors, and in particular for superenergy spinors, are much less transparent and require a lot more effort to establish, when considered from the tensor viewpoint. In this paper we demonstrate how the use of dimensionally dependent tensor identities enables us to derive a number of 4-dimensional identities by straightforward tensor methods in a signature independent manner. In particular, we consider the quadratic identity for the Bel-Robinson tensor ${\cal T}_{abcx}{\cal T}^{abcy} = \delta_x^y {\cal T}_{abcd}{\cal T}^{abcd}/4$ and also the new conservation laws for the Chevreton tensor, both of which have been obtained by spinor means; both of these results are rederived by {\it tensor} means for 4-dimensional spaces of any signature, using dimensionally dependent identities, and also we are able to conclude that there are no {\it direct} higher dimensional analogues. In addition we demonstrate a simple way to show non-existense of such identities via counter examples; in particular we show that there is no non-trivial Bel tensor analogue of this simple Bel-Robinson tensor quadratic identity. On the other hand, as a sample of the power of generalising dimensionally dependent tensor identities from four to higher dimensions, we show that the symmetry structure, trace-free and divergence-free nature of the four dimensional Bel-Robinson tensor does have an analogue for a class of tensors in higher dimensions.Comment: 18 pages; TeX fil

Theoretical Research in Cosmology, High-Energy Physics and String Theory

The research was in the area of Theoretical Physics: Cosmology, High-Energy Physics and String Theor

On Four-Point Functions of Half-BPS Operators in General Dimensions

We study four-point correlation functions of half-BPS operators of arbitrary weight for all dimensions d=3,4,5,6 where superconformal theories exist. Using harmonic superspace techniques, we derive the superconformal Ward identities for these correlators and present them in a universal form. We then solve these identities, employing Jack polynomial expansions. We show that the general solution is parameterized by a set of arbitrary two-variable functions, with the exception of the case d=4, where in addition functions of a single variable appear. We also discuss the operator product expansion using recent results on conformal partial wave amplitudes in arbitrary dimension.Comment: The discussion of the case d=6 expanded; references added/correcte

Scale without Conformal Invariance at Three Loops

We carry out a three-loop computation that establishes the existence of scale without conformal invariance in dimensional regularization with the MS scheme in d=4-epsilon spacetime dimensions. We also comment on the effects of scheme changes in theories with many couplings, as well as in theories that live on non-conformal scale-invariant renormalization group trajectories. Stability properties of such trajectories are analyzed, revealing both attractive and repulsive directions in a specific example. We explain how our results are in accord with those of Jack & Osborn on a c-theorem in d=4 (and d=4-epsilon) dimensions. Finally, we point out that limit cycles with turning points are unlike limit cycles with continuous scale invariance.Comment: 21 pages, 3 figures, Erratum adde

A systematic review of sport and dance participation in healthy young people (15-24 years) to promote subjective wellbeing

We know that taking part in physical activity like sport and dance can bring wellbeing benefits, such as being more satisfied with life and happier, and feeling less anxious and depressed. Most of the evidence is however about adults. This review was carried out to investigate the relationships between subjective wellbeing (SWB) and taking part in sport and dance for healthy young people (15-24 years). Healthy people were defined as those without a condition diagnosed by a health professional. SWB describes wellbeing in terms of the good and bad feelings arising from what people do and how they think. The focus of this review was agreed through on-going collaborative engagement with UK-wide stakeholders representing policy, commissioning and managing, service delivery, and scholars from both academic and non-academic organisations. We examined studies from the past 10 years and found that there is limited good quality evidence, and very little conducted in the UK. The review includes published findings from 977 participants across six countries - China, Korea, India, Turkey, Sweden and the USA. In some studies, participants were predominantly female. A wide variety of wellbeing measures were used. The most common form of sport/dance related activity was based on meditative practices (yoga and Baduanjin Qigong). Other physical activities reported included body conditioning, aerobic exercise, dance training, hip hop dance and sports including volleyball, ice skating, Nintendo Wii Active Games. We included evidence from recent unpublished reports (grey literature) produced by or for sport and dance organisations since 2013. Participants in the evaluations were both male and female with a mean age between 13-24 years and were engaged in UK-based programmes of sport and dance. Findings illustrate that depending on activity type and delivery mode, taking part is associated with wellbeing improvements connected to social connectedness, pleasure, sense of purpose, confidence, interpersonal skills, happiness, relaxation, creative skills and expression, aspiration and ambition. Taking part was also associated with negative wellbeing connected to concerns about competency and capability. Overall, the evidence available in this review suggests that yoga-type activities have the potential to improve subjective wellbeing and that group-based and peer supported sport and dance programmes may promote wellbeing enhancement in youth groups. The evidence in this review provides limited promising findings upon which sport and dance programmes for wellbeing improvement could be developed. The lack of evidence identified in this review does not necessarily mean that wellbeing benefits are not accrued from taking part in sport and dance. There is scope to build evidence on wellbeing outcomes of sport and dance in healthy young people through well-designed, rigorous and appropriate research methods which are underpinned by relevant theory and use established methods of analysis

A systematic review of the subjective wellbeing outcomes of engaging with visual arts for adults (“working-age”, 15-64 years) with diagnosed mental health conditions

The importance of the visual arts in contributing to the wellbeing of adults with mental health conditions has been little documented beyond some insightful and influential interventions and exploratory studies. Initiatives such as Arts on Prescription projects have, in the UK provided examples of the positive effects that engagement in artistic and creative activity can have, and some of these have been documented in small-scale studies of interventions. Most of the evidence has been perceived as positive but of limited scale. In this context, this review was carried out to examine in a more focused way the ‘subjective wellbeing’ (SWB) outcomes of engagement with the visual arts for adults with a background history of mental health conditions. SWB embraces both the positive and negative feelings that arise in individuals based on their view of the world, how they think about themselves and others, and what they do in the interactions and practices of everyday life. Adult subjects in the studies included in this review were of ‘working-age’ (15-64 years). The focus of the review and the precise research question were agreed at inception sessions of the research team, and in collaborative engagement with stakeholders in the areas of policy, service-delivery, project and evaluation commissioning, and research and scholarship in the spheres of the visual arts and mental health. Published studies from the past 10 years were studied for the review, and their findings synthesised and integrated into an evaluation of the state of knowledge in the field, in terms of the specifics of the research questions. We found that there is limited high-quality evidence, though case studies from the UK have provided important and consistent findings, corroborated by grey literature that has reported on interventions and projects. The review includes published findings based on data on/from 163 participants across four countries – Australia, Sweden, the UK, and the USA. Overall, female respondents outnumbered male respondents. A wide variety of wellbeing measures were used in some quantitative, statistical studies. In-depth interviews dominated the qualitative studies, giving voice to the experiences of individual subjects. The visual arts practices that featured in the studies included forms of painting or drawing, art appreciation with selected art forms, artmaking culminating in an exhibition, and more general creative and craft activities that included visual artefacts such as ceramics or sculpture. Evidence we include from recent unpublished reports (grey literature) was produced by or for visual arts organisations since 2014. Participants in the evaluations were both male and female and were engaged in UK-based arts interventions, many via community arts or ‘Arts on Prescription’ types of intervention. Overall, the evidence available in this review has shown that engagement in the visual arts for adults with mental health conditions can reduce reported levels of depression and anxiety; increase self-respect, self-worth and self-esteem; encourage and stimulate re-engagement with the wider, everyday social world; and support in participants a potential renegotiation of identity through practice-based forms of making or doing. The most effective ‘working ways to wellbeing’ are also confirmed in processes of implementation that ensure provision of secure safe-space and havens for interventions; that recognise the value of non-stigmatising settings; and that support and sustain collaborative facilitation of programmes and sessions. 4 Some negative dimensions of engagement with the visual arts were also identified, including stress and pressure felt to complete activities or commit to artmaking, and the very real fear that the end of an intervention would mean the return to a world of anxiety, decreasing confidence and social isolation. The review shows that for adults starting visual arts activities or programmes, the subjective wellbeing outcomes are, for the majority of participants, positive. This applies to men and women alike across the studies. The most convincing evidence has emerged from focused qualitative research designs, and makes clear that the most effective work in the field continues to lack the necessary resources and infrastructure that would ensure sustainable practices and interventions. Overall, there is some evidence of benefit in a weak field that could be strengthened by fuller monitoring of cohorts to evaluate the long-term effects of participants’ engagement with the visual arts

Bose-Einstein condensation for interacting scalar fields in curved spacetime

We consider the model of self-interacting complex scalar fields with a rigid gauge invariance under an arbitrary gauge group $G$. In order to analyze the phenomenon of Bose-Einstein condensation finite temperature and the possibility of a finite background charge is included. Different approaches to derive the relevant high-temperature behaviour of the theory are presented.Comment: 28 pages, LaTe