Phases of a fermionic model with chiral condensates and Cooper pairs in 1+1 dimensions

We study the phase structure of a 4-fermi model with three bare coupling constants, which potentially has three types of bound states. This model is a generalization of the model discussed previously by A. Chodos et al. [Phys. Rev. D 61, 045011 (2000)], which contained both chiral condensates and Cooper pairs. For this generalization we find that there are two independent renormalized coupling constants which determine the phase structure at finite density and temperature. We find that the vacuum can be in one of three distinct phases depending on the value of these two renormalized coupling constants

On the mean-field spherical model

Exact solutions are obtained for the mean-field spherical model, with or without an external magnetic field, for any finite or infinite number N of degrees of freedom, both in the microcanonical and in the canonical ensemble. The canonical result allows for an exact discussion of the loci of the Fisher zeros of the canonical partition function. The microcanonical entropy is found to be nonanalytic for arbitrary finite N. The mean-field spherical model of finite size N is shown to be equivalent to a mixed isovector/isotensor sigma-model on a lattice of two sites. Partial equivalence of statistical ensembles is observed for the mean-field spherical model in the thermodynamic limit. A discussion of the topology of certain state space submanifolds yields insights into the relation of these topological quantities to the thermodynamic behavior of the system in the presence of ensemble nonequivalence.Comment: 21 pages, 5 figure

Chiral Modulations in Curved Space I: Formalism

The goal of this paper is to present a formalism that allows to handle four-fermion effective theories at finite temperature and density in curved space. The formalism is based on the use of the effective action and zeta function regularization, supports the inclusion of inhomogeneous and anisotropic phases. One of the key points of the method is the use of a non-perturbative ansatz for the heat-kernel that returns the effective action in partially resummed form, providing a way to go beyond the approximations based on the Ginzburg-Landau expansion for the partition function. The effective action for the case of ultra-static Riemannian spacetimes with compact spatial section is discussed in general and a series representation, valid when the chemical potential satisfies a certain constraint, is derived. To see the formalism at work, we consider the case of static Einstein spaces at zero chemical potential. Although in this case we expect inhomogeneous phases to occur only as meta-stable states, the problem is complex enough and allows to illustrate how to implement numerical studies of inhomogeneous phases in curved space. Finally, we extend the formalism to include arbitrary chemical potentials and obtain the analytical continuation of the effective action in curved space.Comment: 22 pages, 3 figures; version to appear in JHE

SNPs in Multi-Species Conserved Sequences (MCS) as useful markers in association studies: a practical approach

<p>Abstract</p> <p>Background</p> <p>Although genes play a key role in many complex diseases, the specific genes involved in most complex diseases remain largely unidentified. Their discovery will hinge on the identification of key sequence variants that are conclusively associated with disease. While much attention has been focused on variants in protein-coding DNA, variants in noncoding regions may also play many important roles in complex disease by altering gene regulation. Since the vast majority of noncoding genomic sequence is of unknown function, this increases the challenge of identifying "functional" variants that cause disease. However, evolutionary conservation can be used as a guide to indicate regions of noncoding or coding DNA that are likely to have biological function, and thus may be more likely to harbor SNP variants with functional consequences. To help bias marker selection in favor of such variants, we devised a process that prioritizes annotated SNPs for genotyping studies based on their location within Multi-species Conserved Sequences (MCSs) and used this process to select SNPs in a region of linkage to a complex disease. This allowed us to evaluate the utility of the chosen SNPs for further association studies. Previously, a region of chromosome 1q43 was linked to Multiple Sclerosis (MS) in a genome-wide screen. We chose annotated SNPs in the region based on location within MCSs (termed MCS-SNPs). We then obtained genotypes for 478 MCS-SNPs in 989 individuals from MS families.</p> <p>Results</p> <p>Analysis of our MCS-SNP genotypes from the 1q43 region and comparison to HapMap data confirmed that annotated SNPs in MCS regions are frequently polymorphic and show subtle signatures of selective pressure, consistent with previous reports of genome-wide variation in conserved regions. We also present an online tool that allows MCS data to be directly exported to the UCSC genome browser so that MCS-SNPs can be easily identified within genomic regions of interest.</p> <p>Conclusion</p> <p>Our results showed that MCS can easily be used to prioritize markers for follow-up and candidate gene association studies. We believe that this novel approach demonstrates a paradigm for expediting the search for genes contributing to complex diseases.</p

Generating Functions for Coherent Intertwiners

We study generating functions for the scalar products of SU(2) coherent intertwiners, which can be interpreted as coherent spin network evaluations on a 2-vertex graph. We show that these generating functions are exactly summable for different choices of combinatorial weights. Moreover, we identify one choice of weight distinguished thanks to its geometric interpretation. As an example of dynamics, we consider the simple case of SU(2) flatness and describe the corresponding Hamiltonian constraint whose quantization on coherent intertwiners leads to partial differential equations that we solve. Furthermore, we generalize explicitly these Wheeler-DeWitt equations for SU(2) flatness on coherent spin networks for arbitrary graphs.Comment: 31 page

Nonanalyticities of the entropy induced by saddle points of the potential energy landscape

The relation between saddle points of the potential of a classical many-particle system and the analyticity properties of its Boltzmann entropy is studied. For finite systems, each saddle point is found to cause a nonanalyticity in the Boltzmann entropy, and the functional form of this nonanalytic term is derived for the generic case of potentials having the Morse property. With increasing system size the order of the nonanalytic term grows unboundedly, leading to an increasing differentiability of the entropy. Nonetheless, a distribution of an unboundedly growing number of saddle points may cause a phase transition in the thermodynamic limit. Analyzing the contribution of the saddle points to the density of states in the thermodynamic limit, conditions on the distribution of saddle points and their curvatures are derived which are necessary for a phase transition to occur. With these results, the puzzling absence of topological signatures in the spherical model is elucidated. As further applications, the phase transitions of the mean-field XY model and the mean-field k-trigonometric model are shown to be induced by saddle points of vanishing curvature.Comment: 24 pages, 2 figure

Multi-Regge kinematics and the moduli space of Riemann spheres with marked points

We show that scattering amplitudes in planar N = 4 Super Yang-Mills in multi-Regge kinematics can naturally be expressed in terms of single-valued iterated integrals on the moduli space of Riemann spheres with marked points. As a consequence, scattering amplitudes in this limit can be expressed as convolutions that can easily be computed using Stokes' theorem. We apply this framework to MHV amplitudes to leading-logarithmic accuracy (LLA), and we prove that at L loops all MHV amplitudes are determined by amplitudes with up to L + 4 external legs. We also investigate non-MHV amplitudes, and we show that they can be obtained by convoluting the MHV results with a certain helicity flip kernel. We classify all leading singularities that appear at LLA in the Regge limit for arbitrary helicity configurations and any number of external legs. Finally, we use our new framework to obtain explicit analytic results at LLA for all MHV amplitudes up to five loops and all non-MHV amplitudes with up to eight external legs and four loops.Comment: 104 pages, six awesome figures and ancillary files containing the results in Mathematica forma

From DNA sequence to application: possibilities and complications

The development of sophisticated genetic tools during the past 15 years have facilitated a tremendous increase of fundamental and application-oriented knowledge of lactic acid bacteria (LAB) and their bacteriophages. This knowledge relates both to the assignments of open reading frames (ORF’s) and the function of non-coding DNA sequences. Comparison of the complete nucleotide sequences of several LAB bacteriophages has revealed that their chromosomes have a fixed, modular structure, each module having a set of genes involved in a specific phase of the bacteriophage life cycle. LAB bacteriophage genes and DNA sequences have been used for the construction of temperature-inducible gene expression systems, gene-integration systems, and bacteriophage defence systems. The function of several LAB open reading frames and transcriptional units have been identified and characterized in detail. Many of these could find practical applications, such as induced lysis of LAB to enhance cheese ripening and re-routing of carbon fluxes for the production of a specific amino acid enantiomer. More knowledge has also become available concerning the function and structure of non-coding DNA positioned at or in the vicinity of promoters. In several cases the mRNA produced from this DNA contains a transcriptional terminator-antiterminator pair, in which the antiterminator can be stabilized either by uncharged tRNA or by interaction with a regulatory protein, thus preventing formation of the terminator so that mRNA elongation can proceed. Evidence has accumulated showing that also in LAB carbon catabolite repression in LAB is mediated by specific DNA elements in the vicinity of promoters governing the transcription of catabolic operons. Although some biological barriers have yet to be solved, the vast body of scientific information presently available allows the construction of tailor-made genetically modified LAB. Today, it appears that societal constraints rather than biological hurdles impede the use of genetically modified LAB.