Center Vortices and the Gribov Horizon

We show how the infinite color-Coulomb energy of color-charged states is related to enhanced density of near-zero modes of the Faddeev-Popov operator, and calculate this density numerically for both pure Yang-Mills and gauge-Higgs systems at zero temperature, and for pure gauge theory in the deconfined phase. We find that the enhancement of the eigenvalue density is tied to the presence of percolating center vortex configurations, and that this property disappears when center vortices are either removed from the lattice configurations, or cease to percolate. We further demonstrate that thin center vortices have a special geometrical status in gauge-field configuration space: Thin vortices are located at conical or wedge singularities on the Gribov horizon. We show that the Gribov region is itself a convex manifold in lattice configuration space. The Coulomb gauge condition also has a special status; it is shown to be an attractive fixed point of a more general gauge condition, interpolating between the Coulomb and Landau gauges.Comment: 19 pages, 17 EPS figures, RevTeX4; v2: added references, corrected caption of fig. 11; v3: new data for higher couplings, clarifications on color-Coulomb potential in deconfined phase, version to appear in JHE

Indirect lattice evidence for the Refined Gribov-Zwanziger formalism and the gluon condensate ⟨A2⟩\braket{A^2} in the Landau gauge

We consider the gluon propagator $D(p^2)$ at various lattice sizes and spacings in the case of pure SU(3) Yang-Mills gauge theories using the Landau gauge fixing. We discuss a class of fits in the infrared region in order to (in)validate the tree level analytical prediction in terms of the (Refined) Gribov-Zwanziger framework. It turns out that an important role is played by the presence of the widely studied dimension two gluon condensate $\braket{A^2}$. Including this effect allows to obtain an acceptable fit up to 1 \'{a} 1.5 GeV, while corroborating the Refined Gribov-Zwanziger prediction for the gluon propagator. We also discuss the infinite volume extrapolation, leading to the estimate $D(0)=8.3\pm0.5\text{GeV}^{-2}$. As a byproduct, we can also provide the prediction $\braket{g^2 A^2}\approx 3\text{GeV}^2$ obtained at the renormalization scale $\mu=10\text{GeV}$.Comment: 17 pages, 10 figures, updated version, accepted for publication in Phs.Rev.

Poisson-Lie group of pseudodifferential symbols

We introduce a Lie bialgebra structure on the central extension of the Lie algebra of differential operators on the line and the circle (with scalar or matrix coefficients). This defines a Poisson--Lie structure on the dual group of pseudodifferential symbols of an arbitrary real (or complex) order. We show that the usual (second) Benney, KdV (or GL_n--Adler--Gelfand--Dickey) and KP Poisson structures are naturally realized as restrictions of this Poisson structure to submanifolds of this ``universal'' Poisson--Lie group. Moreover, the reduced (=SL_n) versions of these manifolds (W_n-algebras in physical terminology) can be viewed as subspaces of the quotient (or Poisson reduction) of this Poisson--Lie group by the dressing action of the group of functions. Finally, we define an infinite set of functions in involution on the Poisson--Lie group that give the standard families of Hamiltonians when restricted to the submanifolds mentioned above. The Poisson structure and Hamiltonians on the whole group interpolate between the Poisson structures and Hamiltonians of Benney, KP and KdV flows. We also discuss the geometrical meaning of W_\infty as a limit of Poisson algebras W_\epsilon as \epsilon goes to 0.Comment: 64 pages, no figure

A refinement of the Gribov-Zwanziger approach in the Landau gauge: infrared propagators in harmony with the lattice results

Recent lattice data have reported an infrared suppressed, positivity violating gluon propagator which is nonvanishing at zero momentum and a ghost propagator which is no longer enhanced. This paper discusses how to obtain analytical results which are in qualitative agreement with these lattice data within the Gribov-Zwanziger framework. This framework allows one to take into account effects related to the existence of gauge copies, by restricting the domain of integration in the path integral to the Gribov region. We elaborate to great extent on a previous short paper by presenting additional results, also confirmed by the numerical simulations. A detailed discussion on the soft breaking of the BRST symmetry arising in the Gribov-Zwanziger approach is provided.Comment: 38 pages, 9 figures, the content of section V has been extended and adapte

A study of the gauge invariant, nonlocal mass operator Tr∫d4xFμν(D2)−1FμνTr \int d^4x F_{\mu\nu}(D^2)^{-1} F_{\mu\nu} in Yang-Mills theories

The nonlocal mass operator $Tr \int d^4x F_{\mu\nu} (D^2)^{-1} F_{\mu\nu}$ is considered in Yang-Mills theories in Euclidean space-time. It is shown that the operator $Tr \int d^4x F_{\mu\nu} (D^2)^{-1} F_{\mu\nu}$ can be cast in local form through the introduction of a set of additional fields. A local and polynomial action is thus identified. Its multiplicative renormalizability is proven by means of the algebraic renormalization in the class of linear covariant gauges. The anomalous dimensions of the fields and of the mass operator are computed at one loop order. A few remarks on the possible role of this operator for the issue of the gauge invariance of the dimension two condensates are outlined.Comment: 34 page

Lifetime Racism and Blood Pressure Changes During Pregnancy: Implications for Fetal Growth

Objective: Research suggests that exposure to racism partially explains why African American women are 2 to 3 times more likely to deliver low birth weight and preterm infants. However, the physiological pathways by which racism exerts these effects are unclear. This study examined how lifetime exposure to racism, in combination with maternal blood pressure changes during pregnancy, was associated with fetal growth. Methods: African American pregnant women (n = 39) reported exposure to childhood and adulthood racism in several life domains (e.g., at school, at work), which were experienced directly or indirectly, meaning vicariously experienced when someone close to them was treated unfairly. A research nurse measured maternal blood pressure at 18 to 20 and 30 to 32 weeks gestation. Standardized questionnaires and trained interviewers assessed maternal demographics. Neonatal length of gestation and birth weight data were collected from medical charts. Results: Childhood racism interacted with diastolic blood pressure to predict birth weight. Specifically, women with two or more domains of indirect exposure to racism in childhood and increases in diastolic blood pressure between 18 and 32 weeks had lower gestational age adjusted birth weight than the other women. A similar pattern was found for direct exposure to racism in childhood. Conclusions: Increases in diastolic blood pressure between the second and third trimesters predicted lower birth weight, but only when racism exposure in childhood (direct or indirect) was relatively high. Understanding pregnant African American women’s lifetime direct and indirect experiences with racism in combination with prenatal blood pressure may improve identification of highest risk subgroups within this population

Stress and Blood Pressure During Pregnancy: Racial Differences and Associations With Birthweight

OBJECTIVE: To extend findings that African American women report greater stress during pregnancy, have higher blood pressure (BP), and are twice as likely to have low birthweight infants relative to white women. This study examines a) racial differences in associations between stress and BP during pregnancy, and b) the combined effects of stress and BP on infant birthweight in a sample of 170 African American and white women. METHODS: A prospective, longitudinal study of pregnant women was conducted in which measures of BP, stress, and other relevant variables were collected. Multiple measures of systolic and diastolic BP were taken at each of three points during pregnancy (18-20, 24-26, and 30-32 weeks gestation). RESULTS: Both systolic blood pressure (SBP) and diastolic blood pressure (DBP) were positively associated with stress in pregnant African American women and not in pregnant white women. In analyses of birthweight, there were no main effects of BP or stress. However, a significant interaction demonstrated that, when stress was high, DBP was negatively associated with birthweight and a combination of high stress and high DBP predicted the lowest birthweight in the sample. Furthermore, African American women were twice as likely as white women to have a combination of high stress and high DBP. CONCLUSIONS: Racial differences in relationships between stress and BP, and the interactive effect of stress and DBP on birthweight together suggest that a high stress-high BP profile may pose a risk for lower birthweight among African American women, in particular, and possibly for all pregnant women

Communalism Predicts Prenatal Affect, Stress, and Physiology Better than Ethnicity and Socioeconomic Status

The authors examined the relevance of communalism, operationalized as a cultural orientation emphasizing interdependence, to maternal prenatal emotional health and physiology and distinguished its effects from those of ethnicity and childhood and adult socioeconomic status (SES). African American and European American women (N = 297) were recruited early in pregnancy and followed through 32 weeks gestation using interviews and medical chart review. Overall, African American women and women of lower socioeconomic backgrounds had higher levels of negative affect, stress, and blood pressure, but these ethnic and socioeconomic disparities were not observed among women higher in communalism. Hierarchical multivariate regression analyses showed that communalism was a more robust predictor of prenatal emotional health than ethnicity, childhood SES, and adult SES. Communalism also interacted with ethnicity and SES, resulting in lower blood pressure during pregnancy for African American women and women who experienced socioeconomic disadvantage over the life course. The effects of communalism on prenatal affect, stress, and physiology were not explained by depressive symptoms at study entry, perceived availability of social support, self-esteem, optimism, mastery, nor pregnancy-specific factors, including whether the pregnancy was planned, whether the pregnancy was desired after conception, or how frequently the woman felt happy to be pregnant. This suggests that a communal cultural orientation benefits maternal prenatal emotional health and physiology over and above its links to better understood personal and social resources in addition to economic resources. Implications of culture as a determinant of maternal prenatal health and well-being and an important lens for examining ethnic and socioeconomic inequalities in health are discussed

A2(2)A_{2}^{(2)} Gaudin model and its associated Knizhnik-Zamolodchikov equation

The semiclassical limit of the algebraic Bethe Ansatz for the Izergin-Korepin 19-vertex model is used to solve the theory of Gaudin models associated with the twisted $A_{2}^{(2)}$ R-matrix. We find the spectra and eigenvectors of the $N-1$ independents Gaudin Hamiltonians. We also use the off-shell Bethe Ansatz method to show how the off-shell Gaudin equation solves the associated trigonometric system of Knizhnik-Zamolodchikov equations.Comment: 20 pages,no figure, typos corrected, LaTe

osp(1∣2)osp(1|2) off-shell Bethe ansatz equation with boundary terms

This work is concerned with the quasi-classical limit of the boundary quantum inverse scattering method for the $osp(1|2)$ vertex model with diagonal $K$-matrices. In this limit Gaudin's Hamiltonians with boundary terms are presented and diagonalized. Moreover, integral representations for correlation functions are realized to be solutions of the trigonometric Knizhnik-Zamoldchikov equations.Comment: 38 pages, minor revison, LaTe