Symmetry Nonrestoration in a Gross-Neveu Model with Random Chemical Potential

We study the symmetry behavior of the Gross-Neveu model in three and two dimensions with random chemical potential. This is equivalent to a four-fermion model with charge conjugation symmetry as well as Z_2 chiral symmetry. At high temperature the Z_2 chiral symmetry is always restored. In three dimensions the initially broken charge conjugation symmetry is not restored at high temperature, irrespective of the value of the disorder strength. In two dimensions and at zero temperature the charge conjugation symmetry undergoes a quantum phase transition from a symmetric state (for weak disorder) to a broken state (for strong disorder) as the disorder strength is varied. For any given value of disorder strength, the high-temperature behavior of the charge conjugation symmetry is the same as its zero-temperature behavior. Therefore, in two dimensions and for strong disorder strength the charge conjugation symmetry is not restored at high temperature.Comment: 16 pages, 3 figure

Lectures on the functional renormalization group method

These introductory notes are about functional renormalization group equations and some of their applications. It is emphasised that the applicability of this method extends well beyond critical systems, it actually provides us a general purpose algorithm to solve strongly coupled quantum field theories. The renormalization group equation of F. Wegner and A. Houghton is shown to resum the loop-expansion. Another version, due to J. Polchinski, is obtained by the method of collective coordinates and can be used for the resummation of the perturbation series. The genuinely non-perturbative evolution equation is obtained in a manner reminiscent of the Schwinger-Dyson equations. Two variants of this scheme are presented where the scale which determines the order of the successive elimination of the modes is extracted from external and internal spaces. The renormalization of composite operators is discussed briefly as an alternative way to arrive at the renormalization group equation. The scaling laws and fixed points are considered from local and global points of view. Instability induced renormalization and new scaling laws are shown to occur in the symmetry broken phase of the scalar theory. The flattening of the effective potential of a compact variable is demonstrated in case of the sine-Gordon model. Finally, a manifestly gauge invariant evolution equation is given for QED.Comment: 47 pages, 11 figures, final versio

Confining QCD Strings, Casimir Scaling, and a Euclidean Approach to High-Energy Scattering

We compute the chromo-field distributions of static color-dipoles in the fundamental and adjoint representation of SU(Nc) in the loop-loop correlation model and find Casimir scaling in agreement with recent lattice results. Our model combines perturbative gluon exchange with the non-perturbative stochastic vacuum model which leads to confinement of the color-charges in the dipole via a string of color-fields. We compute the energy stored in the confining string and use low-energy theorems to show consistency with the static quark-antiquark potential. We generalize Meggiolaro's analytic continuation from parton-parton to gauge-invariant dipole-dipole scattering and obtain a Euclidean approach to high-energy scattering that allows us in principle to calculate S-matrix elements directly in lattice simulations of QCD. We apply this approach and compute the S-matrix element for high-energy dipole-dipole scattering with the presented Euclidean loop-loop correlation model. The result confirms the analytic continuation of the gluon field strength correlator used in all earlier applications of the stochastic vacuum model to high-energy scattering.Comment: 65 pages, 13 figures, extended and revised version to be published in Phys. Rev. D (results unchanged, 2 new figures, 1 new table, additional discussions in Sec.2.3 and Sec.5, new appendix on the non-Abelian Stokes theorem, old Appendix A -> Sec.3, several references added

Structural brain alterations associated with suicidal thoughts and behaviors in young people: results from 21 international studies from the ENIGMA Suicidal Thoughts and Behaviours consortium

Identifying brain alterations associated with suicidal thoughts and behaviors (STBs) in young people is critical to understanding their development and improving early intervention and prevention. The ENIGMA Suicidal Thoughts and Behaviours (ENIGMA-STB) consortium analyzed neuroimaging data harmonized across sites to examine brain morphology associated with STBs in youth. We performed analyses in three separate stages, in samples ranging from most to least homogeneous in terms of suicide assessment instrument and mental disorder. First, in a sample of 577 young people with mood disorders, in which STBs were assessed with the Columbia Suicide Severity Rating Scale (C-SSRS). Second, in a sample of young people with mood disorders, in which STB were assessed using different instruments, MRI metrics were compared among healthy controls without STBs (HC; N = 519), clinical controls with a mood disorder but without STBs (CC; N = 246) and young people with current suicidal ideation (N = 223). In separate analyses, MRI metrics were compared among HCs (N = 253), CCs (N = 217), and suicide attempters (N = 64). Third, in a larger transdiagnostic sample with various assessment instruments (HC = 606; CC = 419; Ideation = 289; HC = 253; CC = 432; Attempt=91). In the homogeneous C-SSRS sample, surface area of the frontal pole was lower in young people with mood disorders and a history of actual suicide attempts (N = 163) than those without a lifetime suicide attempt (N = 323; FDR-p = 0.035, Cohen's d = 0.34). No associations with suicidal ideation were found. When examining more heterogeneous samples, we did not observe significant associations. Lower frontal pole surface area may represent a vulnerability for a (non-interrupted and non-aborted) suicide attempt; however, more research is needed to understand the nature of its relationship to suicide risk.New methods for child psychiatric diagnosis and treatment outcome evaluatio

Large-scale analysis of structural brain asymmetries in schizophrenia via the ENIGMA consortium.

Left-right asymmetry is an important organizing feature of the healthy brain that may be altered in schizophrenia, but most studies have used relatively small samples and heterogeneous approaches, resulting in equivocal findings. We carried out the largest case-control study of structural brain asymmetries in schizophrenia, with MRI data from 5,080 affected individuals and 6,015 controls across 46 datasets, using a single image analysis protocol. Asymmetry indexes were calculated for global and regional cortical thickness, surface area, and subcortical volume measures. Differences of asymmetry were calculated between affected individuals and controls per dataset, and effect sizes were meta-analyzed across datasets. Small average case-control differences were observed for thickness asymmetries of the rostral anterior cingulate and the middle temporal gyrus, both driven by thinner left-hemispheric cortices in schizophrenia. Analyses of these asymmetries with respect to the use of antipsychotic medication and other clinical variables did not show any significant associations. Assessment of age- and sex-specific effects revealed a stronger average leftward asymmetry of pallidum volume between older cases and controls. Case-control differences in a multivariate context were assessed in a subset of the data (N = 2,029), which revealed that 7% of the variance across all structural asymmetries was explained by case-control status. Subtle case-control differences of brain macrostructural asymmetry may reflect differences at the molecular, cytoarchitectonic, or circuit levels that have functional relevance for the disorder. Reduced left middle temporal cortical thickness is consistent with altered left-hemisphere language network organization in schizophrenia