Limit Cycles and Conformal Invariance

There is a widely held belief that conformal field theories (CFTs) require zero beta functions. Nevertheless, the work of Jack and Osborn implies that the beta functions are not actually the quantites that decide conformality, but until recently no such behavior had been exhibited. Our recent work has led to the discovery of CFTs with nonzero beta functions, more precisely CFTs that live on recurrent trajectories, e.g., limit cycles, of the beta-function vector field. To demonstrate this we study the S function of Jack and Osborn. We use Weyl consistency conditions to show that it vanishes at fixed points and agrees with the generator Q of limit cycles on them. Moreover, we compute S to third order in perturbation theory, and explicitly verify that it agrees with our previous determinations of Q. A byproduct of our analysis is that, in perturbation theory, unitarity and scale invariance imply conformal invariance in four-dimensional quantum field theories. Finally, we study some properties of these new, "cyclic" CFTs, and point out that the a-theorem still governs the asymptotic behavior of renormalization-group flows.Comment: 31 pages, 4 figures. Expanded introduction to make clear that cycles discussed in this work are not associated with unitary theories that are scale but not conformally invarian

Limit Cycles in Four Dimensions

We present an example of a limit cycle, i.e., a recurrent flow-line of the beta-function vector field, in a unitary four-dimensional gauge theory. We thus prove that beta functions of four-dimensional gauge theories do not produce gradient flows. The limit cycle is established in perturbation theory with a three-loop calculation which we describe in detail.Comment: 12 pages, 1 figure. Significant revision of the interpretation of our result. Improved description of three-loop calculatio

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

On renormalization group flows and the a-theorem in 6d

We study the extension of the approach to the a-theorem of Komargodski and Schwimmer to quantum field theories in d=6 spacetime dimensions. The dilaton effective action is obtained up to 6th order in derivatives. The anomaly flow a_UV - a_IR is the coefficient of the 6-derivative Euler anomaly term in this action. It then appears at order p^6 in the low energy limit of n-point scattering amplitudes of the dilaton for n > 3. The detailed structure with the correct anomaly coefficient is confirmed by direct calculation in two examples: (i) the case of explicitly broken conformal symmetry is illustrated by the free massive scalar field, and (ii) the case of spontaneously broken conformal symmetry is demonstrated by the (2,0) theory on the Coulomb branch. In the latter example, the dilaton is a dynamical field so 4-derivative terms in the action also affect n-point amplitudes at order p^6. The calculation in the (2,0) theory is done by analyzing an M5-brane probe in AdS_7 x S^4. Given the confirmation in two distinct models, we attempt to use dispersion relations to prove that the anomaly flow is positive in general. Unfortunately the 4-point matrix element of the Euler anomaly is proportional to stu and vanishes for forward scattering. Thus the optical theorem cannot be applied to show positivity. Instead the anomaly flow is given by a dispersion sum rule in which the integrand does not have definite sign. It may be possible to base a proof of the a-theorem on the analyticity and unitarity properties of the 6-point function, but our preliminary study reveals some difficulties.Comment: 41 pages, 5 figure

Multimorbidity and comorbidity in the Dutch population - data from general practices

<p>Abstract</p> <p>Background</p> <p>Multimorbidity is increasingly recognized as a major public health challenge of modern societies. However, knowledge about the size of the population suffering from multimorbidity and the type of multimorbidity is scarce. The objective of this study was to present an overview of the prevalence of multimorbidity and comorbidity of chronic diseases in the Dutch population and to explore disease clustering and common comorbidities.</p> <p>Methods</p> <p>We used 7 years data (2002–2008) of a large Dutch representative network of general practices (212,902 patients). Multimorbidity was defined as having two or more out of 29 chronic diseases. The prevalence of multimorbidity was calculated for the total population and by sex and age group. For 10 prevalent diseases among patients of 55 years and older (N = 52,014) logistic regressions analyses were used to study disease clustering and descriptive analyses to explore common comorbid diseases.</p> <p>Results</p> <p>Multimorbidity of chronic diseases was found among 13% of the Dutch population and in 37% of those older than 55 years. Among patients over 55 years with a specific chronic disease more than two-thirds also had one or more other chronic diseases. Most disease pairs occurred more frequently than would be expected if diseases had been independent. Comorbidity was not limited to specific combinations of diseases; about 70% of those with a disease had one or more extra chronic diseases recorded which were not included in the top five of most common diseases.</p> <p>Conclusion</p> <p>Multimorbidity is common at all ages though increasing with age, with over two-thirds of those with chronic diseases and aged 55 years and older being recorded with multimorbidity. Comorbidity encompassed many different combinations of chronic diseases. Given the ageing population, multimorbidity and its consequences should be taken into account in the organization of care in order to avoid fragmented care, in medical research and healthcare policy.</p

Interferon regulatory factor 8-deficiency determines massive neutrophil recruitment but T cell defect in fast growing granulomas during tuberculosis

Following Mycobacterium tuberculosis (Mtb) infection, immune cell recruitment in lungs is pivotal in establishing protective immunity through granuloma formation and neogenesis of lymphoid structures (LS). Interferon regulatory factor-8 (IRF-8) plays an important role in host defense against Mtb, although the mechanisms driving anti-mycobacterial immunity remain unclear. In this study, IRF-8 deficient mice (IRF-8−/−) were aerogenously infected with a low-dose Mtb Erdman virulent strain and the course of infection was compared with that induced in wild-type (WT-B6) counterparts. Tuberculosis (TB) progression was examined in both groups using pathological, microbiological and immunological parameters. Following Mtb exposure, the bacterial load in lungs and spleens progressed comparably in the two groups for two weeks, after which IRF-8−/− mice developed a fatal acute TB whereas in WT-B6 the disease reached a chronic stage. In lungs of IRF-8−/−, uncontrolled growth of pulmonary granulomas and impaired development of LS were observed, associated with unbalanced homeostatic chemokines, progressive loss of infiltrating T lymphocytes and massive prevalence of neutrophils at late infection stages. Our data define IRF-8 as an essential factor for the maintenance of proper immune cell recruitment in granulomas and LS required to restrain Mtb infection. Moreover, IRF-8−/− mice, relying on a common human and mouse genetic mutation linked to susceptibility/severity of mycobacterial diseases, represent a valuable model of acute TB for comparative studies with chronically-infected congenic WT-B6 for dissecting protective and pathological immune reactions

Light dark matter and Z′Z' dark force at colliders

Light Dark Matter, $<10$ GeV, with sizable direct detection rate is an interesting and less explored scenario. Collider searches can be very powerful, such as through the channel in which a pair of dark matter particle are produced in association with a jet. It is a generic possibility that the mediator of the interaction between DM and the nucleus will also be accessible at the Tevatron and the LHC. Therefore, collider search of the mediator can provide a more comprehensive probe of the dark matter and its interactions. In this article, to demonstrate the complementarity of these two approaches, we focus on the possibility of the mediator being a new $U(1)'$ gauge boson, which is probably the simplest model which allows a large direct detection cross section for a light dark matter candidate. We combine searches in the monojet+MET channel and dijet resonance search for the mediator. We find that for the mass of $Z'$ between 250 GeV and 4 TeV, resonance searches at the colliders provide stronger constraints on this model than the monojet+MET searches.Comment: 23 pages and 14 figure

Comments on Holographic Entanglement Entropy and RG Flows

Using holographic entanglement entropy for strip geometry, we construct a candidate for a c-function in arbitrary dimensions. For holographic theories dual to Einstein gravity, this c-function is shown to decrease monotonically along RG flows. A sufficient condition required for this monotonic flow is that the stress tensor of the matter fields driving the holographic RG flow must satisfy the null energy condition over the holographic surface used to calculate the entanglement entropy. In the case where the bulk theory is described by Gauss-Bonnet gravity, the latter condition alone is not sufficient to establish the monotonic flow of the c-function. We also observe that for certain holographic RG flows, the entanglement entropy undergoes a 'phase transition' as the size of the system grows and as a result, evolution of the c-function may exhibit a discontinuous drop.Comment: 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

Fermi Gamma-ray Imaging of a Radio Galaxy

The Fermi Gamma-ray Space Telescope has detected the gamma-ray glow emanating from the giant radio lobes of the radio galaxy Centaurus A. The resolved gamma-ray image shows the lobes clearly separated from the central active source. In contrast to all other active galaxies detected so far in high-energy gamma-rays, the lobe flux constitutes a considerable portion (>1/2) of the total source emission. The gamma-ray emission from the lobes is interpreted as inverse Compton scattered relic radiation from the cosmic microwave background (CMB), with additional contribution at higher energies from the infrared-to-optical extragalactic background light (EBL). These measurements provide gamma-ray constraints on the magnetic field and particle energy content in radio galaxy lobes, and a promising method to probe the cosmic relic photon fields.Comment: 27 pages, includes Supplementary Online Material; corresponding authors: C.C. Cheung, Y. Fukazawa, J. Knodlseder, L. Stawar