Sum rules and three point functions

Sum rules constraining the R-current spectral densities are derived holographically for the case of D3-branes, M2-branes and M5-branes all at finite chemical potentials. In each of the cases the sum rule relates a certain integral of the spectral density over the frequency to terms which depend both on long distance physics, hydrodynamics and short distance physics of the theory. The terms which which depend on the short distance physics result from the presence of certain chiral primaries in the OPE of two R-currents which are turned on at finite chemical potential. Since these sum rules contain information of the OPE they provide an alternate method to obtain the structure constants of the two R-currents and the chiral primary. As a consistency check we show that the 3 point function derived from the sum rule precisely matches with that obtained using Witten diagrams.Comment: 41 page

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

Holographic non-relativistic fermionic fixed point by the charged dilatonic black hole

Driven by the landscape of garden-variety condensed matter systems, we have investigated how the dual spectral function behaves at the non-relativistic as well as relativistic fermionic fixed point by considering the probe Dirac fermion in an extremal charged dilatonic black hole with zero entropy. Although the pattern for both of the appearance of flat band and emergence of Fermi surface is qualitatively similar to that given by the probe fermion in the extremal Reissner-Nordstrom AdS black hole, we find a distinctly different low energy behavior around the Fermi surface, which can be traced back to the different near horizon geometry. In particular, with the peculiar near horizon geometry of our extremal charged dilatonic black hole, the low energy behavior exhibits the universal linear dispersion relation and scaling property, where the former indicates that the dual liquid is a Fermi one while the latter implies that the dual liquid is not exactly of Landau Fermi type

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

Three-dimensional assessment of impingement risk in geometrically parameterised hips compared with clinical measures

Abnormal bony morphology is a factor implicated in hip joint soft tissue damage and an increased lifetime risk of osteoarthritis. Standard two-dimensional radiographic measurements for diagnosis of hip deformities, such as cam deformities on the femoral neck, do not capture the full joint geometry and are not indicative of symptomatic damage. In this study, a three-dimensional geometric parameterisation system was developed to capture key variations in the femur and acetabulum of subjects with clinically diagnosed cam deformity. The parameterisation was performed for Computed Tomography scans of 20 patients (10 female, 10 male). Novel quantitative measures of cam deformity were taken and used to assess differences in morphological deformities between males and females. The parametric surfaces matched the more detailed, segmented hip bone geometry with low fitting error. The quantitative severity measures captured both the size and position of cams, and distinguished between cam and control femurs. The precision of the measures was sufficient to identify differences between subjects that could not be seen with the sole use of two-dimensional imaging. In particular, cams were found to be more superiorly located in males than in females. As well as providing a means to distinguish between subjects more clearly, the new geometric hip parameterisation facilitates the flexible and rapid generation of a range of realistic hip geometries including cams. When combined with material property models, these stratified cam shapes can be used for further assessment of the effect of the geometric variation under impingement conditions

Effective Holographic Theories for low-temperature condensed matter systems

The IR dynamics of effective holographic theories capturing the interplay between charge density and the leading relevant scalar operator at strong coupling are analyzed. Such theories are parameterized by two real exponents $(\gamma,\delta)$ that control the IR dynamics. By studying the thermodynamics, spectra and conductivities of several classes of charged dilatonic black hole solutions that include the charge density back reaction fully, the landscape of such theories in view of condensed matter applications is characterized. Several regions of the $(\gamma,\delta)$ plane can be excluded as the extremal solutions have unacceptable singularities. The classical solutions have generically zero entropy at zero temperature, except when $\gamma=\delta$ where the entropy at extremality is finite. The general scaling of DC resistivity with temperature at low temperature, and AC conductivity at low frequency and temperature across the whole $(\gamma,\delta)$ plane, is found. There is a codimension-one region where the DC resistivity is linear in the temperature. For massive carriers, it is shown that when the scalar operator is not the dilaton, the DC resistivity scales as the heat capacity (and entropy) for planar (3d) systems. Regions are identified where the theory at finite density is a Mott-like insulator at T=0. We also find that at low enough temperatures the entropy due to the charge carriers is generically larger than at zero charge density.Comment: (v3): Added discussion on the UV completion of the solutions, and on extremal spectra in the charged case. Expanded discusion on insulating extremal solutions. Many other refinements and corrections. 126 pages. 48 figure

The Familial Clustering of Age at Menarche in Extended Twin Families

The timing of puberty is complex, possibly involving many genetic factors that may interact with environmental influences. Familial resemblance for age at menarche was studied in a sample of 4,995 female twins, 1,296 sisters, 2,946 mothers and 635 female spouses of male twins. They had indicated their age at menarche as part of a larger longitudinal survey. We assessed assortative mating for age at menarche, gene–environment interaction effects and estimated the heritability of individual differences in pubertal timing. There was significant evidence of gene–environment interaction, accounting for 1.5% of the variance. There was no indication of consistent mate assortment on age at menarche. Individual differences in age at menarche are highly heritable, with additive genetic factors explaining at least 70% of the true variation. An additional 1.5% of the variation can be explained by a genotype–environment interaction effect where environmental factors are more important in individuals genetically predisposed for late menarche

Myocardial ischemia in the absence of epicardial coronary artery disease in Friedreich's ataxia

We present the first in vivo detection of microvascular abnormality in a patient with Friedreich's ataxia (FA) without epicardial coronary artery disease using cardiac magnetic resonance (CMR). The patient had exertional chest pain and dyspnea prompting referral for cardiac evaluation. These symptoms were reproduced during intravenous adenosine infusion, and simultaneous first-pass perfusion imaging showed a significant subendocardial defect; both symptoms and perfusion deficit were absent at rest. Epicardial coronaries were free of disease by invasive angiography; together, these findings support the notion of impaired myocardial perfusion reserve in FA