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

Flexible Bayesian Dynamic Modeling of Correlation and Covariance Matrices

Modeling correlation (and covariance) matrices can be challenging due to the positive-definiteness constraint and potential high-dimensionality. Our approach is to decompose the covariance matrix into the correlation and variance matrices and propose a novel Bayesian framework based on modeling the correlations as products of unit vectors. By specifying a wide range of distributions on a sphere (e.g. the squared-Dirichlet distribution), the proposed approach induces flexible prior distributions for covariance matrices (that go beyond the commonly used inverse-Wishart prior). For modeling real-life spatio-temporal processes with complex dependence structures, we extend our method to dynamic cases and introduce unit-vector Gaussian process priors in order to capture the evolution of correlation among components of a multivariate time series. To handle the intractability of the resulting posterior, we introduce the adaptive $\Delta$-Spherical Hamiltonian Monte Carlo. We demonstrate the validity and flexibility of our proposed framework in a simulation study of periodic processes and an analysis of rat's local field potential activity in a complex sequence memory task.Comment: 49 pages, 15 figure

SM(2,4k) fermionic characters and restricted jagged partitions

A derivation of the basis of states for the $SM(2,4k)$ superconformal minimal models is presented. It relies on a general hypothesis concerning the role of the null field of dimension $2k-1/2$. The basis is expressed solely in terms of $G_r$ modes and it takes the form of simple exclusion conditions (being thus a quasi-particle-type basis). Its elements are in correspondence with $(2k-1)$-restricted jagged partitions. The generating functions of the latter provide novel fermionic forms for the characters of the irreducible representations in both Ramond and Neveu-Schwarz sectors.Comment: 12 page

Neuroconductor: an R platform for medical imaging analysis

Neuroconductor (https://neuroconductor.org) is an open-source platform for rapid testing and dissemination of reproducible computational imaging software. The goals of the project are to: (i) provide a centralized repository of R software dedicated to image analysis, (ii) disseminate software updates quickly, (iii) train a large, diverse community of scientists using detailed tutorials and short courses, (iv) increase software quality via automatic and manual quality controls, and (v) promote reproducibility of image data analysis. Based on the programming language R (https://www.r-project.org/), Neuroconductor starts with 51 inter-operable packages that cover multiple areas of imaging including visualization, data processing and storage, and statistical inference. Neuroconductor accepts new R package submissions, which are subject to a formal review and continuous automated testing. We provide a description of the purpose of Neuroconductor and the user and developer experience

Damping of field-induced chemical potential oscillations in ideal two-band compensated metals

The field and temperature dependence of the de Haas-van Alphen oscillations spectrum is studied for an ideal two-dimensional compensated metal. It is shown that the chemical potential oscillations, involved in the frequency combinations observed in the case of uncompensated orbits, are strongly damped and can even be suppressed when the effective masses of the electron- and hole-type orbits are the same. When magnetic breakdown between bands occurs, this damping is even more pronounced and the Lifshits-Kosevich formalism accounts for the data in a wide field range.Comment: 11 pages, 10 figures, to appear in PR

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

Analytical treatment of the dHvA frequency combinations due to chemical potential oscillations in an idealized two-band Fermi liquid

de Haas-van Alphen oscillation spectrum is studied for an idealized two-dimensional Fermi liquid with two parabolic bands in the case of canonical (fixed number of quasiparticles) and grand canonical (fixed chemical potential) ensembles. As already reported in the literature, oscillations of the chemical potential in magnetic field yield frequency combinations that are forbidden in the framework of the semiclassical theory. Exact analytical calculation of the Fourier components is derived at zero temperature and an asymptotic expansion is given for the high temperature and low magnetic field range. A good agreement is obtained between analytical formulae and numerical computations.Comment: 10 pages, 4 figure

Properties of Non-Abelian Fractional Quantum Hall States at Filling ν=kr\nu=\frac{k}{r}

We compute the physical properties of non-Abelian Fractional Quantum Hall (FQH) states described by Jack polynomials at general filling $\nu=\frac{k}{r}$. For $r=2$, these states are identical to the $Z_k$ Read-Rezayi parafermions, whereas for $r>2$ they represent new FQH states. The $r=k+1$ states, multiplied by a Vandermonde determinant, are a non-Abelian alternative construction of states at fermionic filling $2/5, 3/7, 4/9...$. We obtain the thermal Hall coefficient, the quantum dimensions, the electron scaling exponent, and show that the non-Abelian quasihole has a well-defined propagator falling off with the distance. The clustering properties of the Jack polynomials, provide a strong indication that the states with $r>2$ can be obtained as correlators of fields of \emph{non-unitary} conformal field theories, but the CFT-FQH connection fails when invoked to compute physical properties such as thermal Hall coefficient or, more importantly, the quasihole propagator. The quasihole wavefuntion, when written as a coherent state representation of Jack polynomials, has an identical structure for \emph{all} non-Abelian states at filling $\nu=\frac{k}{r}$.Comment: 2 figure

Recent developments in the determination of the amplitude and phase of quantum oscillations for the linear chain of coupled orbits

De Haas-van Alphen oscillations are studied for Fermi surfaces (FS) illustrating the model proposed by Pippard in the early sixties, namely the linear chain of orbits coupled by magnetic breakdown. This FS topology is relevant for many multiband quasi-two dimensional (q-2D) organic metals such as $\kappa$-(BEDT-TTF)$_2$Cu(NCS)$_2$ and $\theta$-(BEDT-TTF)$_4$CoBr$_4$(C$_6$H$_4$Cl$_2$) which are considered in detail. Whereas the Lifshits-Kosevich model only involves a first order development of field- and temperature-dependent damping factors, second order terms may have significant contribution on the Fourier components amplitude for such q-2D systems at high magnetic field and low temperature. The strength of these second order terms depends on the relative value of the involved damping factors, which are in turns strongly dependent on parameters such as the magnetic breakdown field, effective masses and, most of all, effective Land\'{e} factors. In addition, the influence of field-dependent Onsager phase factors on the oscillation spectra is considered.Comment: arXiv admin note: text overlap with arXiv:1304.665