Bulk spectral function sum rule in QCD-like theories with a holographic dual

We derive the sum rule for the spectral function of the stress-energy tensor in the bulk (uniform dilatation) channel in a general class of strongly coupled field theories. This class includes theories holographically dual to a theory of gravity coupled to a single scalar field, representing the operator of the scale anomaly. In the limit when the operator becomes marginal, the sum rule coincides with that in QCD. Using the holographic model, we verify explicitly the cancellation between large and small frequency contributions to the spectral integral required to satisfy the sum rule in such QCD-like theories.Comment: 16 pages, 2 figure

The clinical assessment study of the foot (CASF): study protocol for a prospective observational study of foot pain and foot osteoarthritis in the general population.

BACKGROUND: Symptomatic osteoarthritis (OA) affects approximately 10% of adults aged over 60 years. The foot joint complex is commonly affected by OA, yet there is relatively little research into OA of the foot, compared with other frequently affected sites such as the knee and hand. Existing epidemiological studies of foot OA have focussed predominantly on the first metatarsophalangeal joint at the expense of other joints. This three-year prospective population-based observational cohort study will describe the prevalence of symptomatic radiographic foot OA, relate its occurrence to symptoms, examination findings and life-style-factors, describe the natural history of foot OA, and examine how it presents to, and is diagnosed and managed in primary care. METHODS: All adults aged 50 years and over registered with four general practices in North Staffordshire, UK, will be invited to participate in a postal Health Survey questionnaire. Respondents to the questionnaire who indicate that they have experienced foot pain in the preceding twelve months will be invited to attend a research clinic for a detailed clinical assessment. This assessment will consist of: clinical interview; physical examination; digital photography of both feet and ankles; plain x-rays of both feet, ankles and hands; ultrasound examination of the plantar fascia; anthropometric measurement; and a further self-complete questionnaire. Follow-up will be undertaken in consenting participants by postal questionnaire at 18 months (clinic attenders only) and three years (clinic attenders and survey participants), and also by review of medical records. DISCUSSION: This three-year prospective epidemiological study will combine survey data, comprehensive clinical, x-ray and ultrasound assessment, and review of primary care records to identify radiographic phenotypes of foot OA in a population of community-dwelling older adults, and describe their impact on symptoms, function and clinical examination findings, and their presentation, diagnosis and management in primary care

Sum rules, plasma frequencies and Hall phenomenology in holographic plasmas

We study the AC optical and hall conductivities of Dp/Dq-branes intersections in the probe approximation and use sum-rules to study various associated transport coefficients. We determine that the presence of massive fundamental matter, as compared to massless fundamental matter described holographically by a theory with no dimensional defects, reduces the plasma frequency. We further show that this is not the case when the brane intersections include defects. We discuss in detail how to implement correctly the regularization of retarded Green's functions so that the dispersion relations are satisfied and the low energy behaviour of the system is physically realistic.Comment: 25 pages, 5 figures. v2.minor changes, published versio

Sum Rules from an Extra Dimension

Using the gravity side of the AdS/CFT correspondence, we investigate the analytic properties of thermal retarded Green's functions for scalars, conserved currents, the stress tensor, and massless fermions. We provide some results concerning their large and small frequency behavior and their pole structure. From these results, it is straightforward to prove the validity of various sum rules on the field theory side of the duality. We introduce a novel contraction mapping we use to study the large frequency behavior of the Green's functions.Comment: v2: 23 pages (plus appendix), revised presentation, discussion of branch cuts moved to appendix, and some minor changes; v1: 24 pages (plus appendix

Transport coefficients, membrane couplings and universality at extremality

We present an efficient method for computing the zero frequency limit of transport coefficients in strongly coupled field theories described holographically by higher derivative gravity theories. Hydrodynamic parameters such as shear viscosity and conductivity can be obtained by computing residues of poles of the off-shell lagrangian density. We clarify in which sense these coefficients can be thought of as effective couplings at the horizon, and present analytic, Wald-like formulae for the shear viscosity and conductivity in a large class of general higher derivative lagrangians. We show how to apply our methods to systems at zero temperature but finite chemical potential. Our results imply that such theories satisfy $\eta/s=1/4\pi$ universally in the Einstein-Maxwell sector. Likewise, the zero frequency limit of the real part of the conductivity for such systems is shown to be universally zero, and we conjecture that higher derivative corrections in this sector do not modify this result to all orders in perturbation theory.Comment: 29 pages, v2: Small text changes for clarity, typos correcte

On The Phase Structure and Thermodynamic Geometry of R-Charged Black Holes

We study the phase structure and equilibrium state space geometry of R-charged black holes in $D = 5$, 4 and 7 and the corresponding rotating $D3$, $M2$ and $M5$ branes. For various charge configurations of the compact black holes in the canonical ensemble we demonstrate new liquid-gas like phase coexistence behaviour culminating in second order critical points. The critical exponents turn out to be the same as that of four dimensional asymptotically AdS black holes in Einstein Maxwell theory. We further establish that the regions of stability for R-charged black holes are, in some cases, more constrained than is currently believed, due to properties of some of the response coefficients. The equilibrium state space scalar curvature is calculated for various charge configurations, both for the case of compact as well as flat horizons and its asymptotic behaviour with temperature is established.Comment: 1 + 33 pages, LaTeX, 25 figures. References adde

The a-theorem and conformal symmetry breaking in holographic RG flows

We study holographic models describing an RG flow between two fixed points driven by a relevant scalar operator. We show how to introduce a spurion field to restore Weyl invariance and compute the anomalous contribution to the generating functional in even dimensional theories. We find that the coefficient of the anomalous term is proportional to the difference of the conformal anomalies of the UV and IR fixed points, as expected from anomaly matching arguments in field theory. For any even dimensions the coefficient is positive as implied by the holographic a-theorem. For flows corresponding to spontaneous breaking of conformal invariance, we also compute the two-point functions of the energy-momentum tensor and the scalar operator and identify the dilaton mode. Surprisingly we find that in the simplest models with just one scalar field there is no dilaton pole in the two-point function of the scalar operator but a stronger singularity. We discuss the possible implications.Comment: 50 pages. v2: minor changes, added references, extended discussion. v3: we have clarified some of the calculations and assumptions, results unchanged. v4: published version in JHE

Demographic and clinical factors associated with radiographic severity of first metatarsophalangeal joint osteoarthritis: cross-sectional findings from the Clinical Assessment Study of the Foot

OBJECTIVE: To explore demographic and clinical factors associated with radiographic severity of first metatarsophalangeal joint osteoarthritis (OA) (First MTPJ OA). DESIGN: Adults aged ≥50 years registered with four general practices were mailed a Health Survey. Responders reporting foot pain within the last 12 months were invited to undergo a clinical assessment and weight-bearing dorso-plantar and lateral radiographs of both feet. Radiographic first MTPJ OA in the most severely affected foot was graded into four categories using a validated atlas. Differences in selected demographic and clinical factors were explored across the four radiographic severity subgroups using analysis of variance (ANOVA) and ordinal regression. RESULTS: Clinical and radiographic data were available from 517 participants, categorised as having no (n = 105), mild (n = 228), moderate (n = 122) or severe (n = 62) first MTPJ OA. Increased radiographic severity was associated with older age and lower educational attainment. After adjusting for age, increased radiographic first MTPJ OA severity was significantly associated with an increased prevalence of dorsal hallux and first MTPJ pain, hallux valgus, first interphalangeal joint (IPJ) hyperextension, keratotic lesions on the dorsal aspect of the hallux and first MTPJ, decreased first MTPJ dorsiflexion, ankle/subtalar joint eversion and ankle joint dorsiflexion range of motion, and a trend towards a more pronated foot posture. CONCLUSIONS: This cross-sectional study has identified several dose-response associations between radiographic severity of first MTPJ OA and a range of demographic and clinical factors. These findings highlight the progressive nature of first MTPJ OA and provide insights into the spectrum of presentation of the condition in clinical practice