Canonical quantization of the WZW model with defects and Chern-Simons theory

We perform canonical quantization of the WZW model with defects and permutation branes. We establish symplectomorphism between phase space of WZW model with $N$ defects on cylinder and phase space of Chern-Simons theory on annulus times $R$ with $N$ Wilson lines, and between phase space of WZW model with $N$ defects on strip and Chern-Simons theory on disc times $R$ with $N+2$ Wilson lines. We obtained also symplectomorphism between phase space of the $N$-fold product of the WZW model with boundary conditions specified by permutation branes, and phase space of Chern-Simons theory on sphere with $N$ holes and two Wilson lines.Comment: 26 pages, minor corrections don

Geometric structures on loop and path spaces

Is is known that the loop space associated to a Riemannian manifold admits a quasi-symplectic structure. This article shows that this structure is not likely to recover the underlying Riemannian metric by proving a result that is a strong indication of the "almost" independence of the quasi-symplectic structure with respect to the metric. Finally conditions to have contact structures on these spaces are studied.Comment: Final version. To appear in Proceedings of Math. Sci. Indian Academy of Science

Catholic Higher Education and Latino(a) Students: Exploring the Experience of University Undergraduates

The experience of Latino(a) undergraduates at Notre Dame was the focus of this study. In general, the students had a positive experience at the university, but one that included challenges, including physical separation from family and familiar community. Family and spiritual supports were important to the Latino(a) students as they coped with difficulties they encountered at the university, than for a comparable sample of Anglo students attending Notre Dame

String theories as the adiabatic limit of Yang-Mills theory

We consider Yang-Mills theory with a matrix gauge group $G$ on a direct product manifold $M=\Sigma_2\times H^2$, where $\Sigma_2$ is a two-dimensional Lorentzian manifold and $H^2$ is a two-dimensional open disc with the boundary $S^1=\partial H^2$. The Euler-Lagrange equations for the metric on $\Sigma_2$ yield constraint equations for the Yang-Mills energy-momentum tensor. We show that in the adiabatic limit, when the metric on $H^2$ is scaled down, the Yang-Mills equations plus constraints on the energy-momentum tensor become the equations describing strings with a worldsheet $\Sigma_2$ moving in the based loop group $\Omega G=C^\infty (S^1, G)/G$, where $S^1$ is the boundary of $H^2$. By choosing $G=R^{d-1, 1}$ and putting to zero all parameters in $\Omega R^{d-1, 1}$ besides $R^{d-1, 1}$, we get a string moving in $R^{d-1, 1}$. In arXiv:1506.02175 it was described how one can obtain the Green-Schwarz superstring action from Yang-Mills theory on $\Sigma_2\times H^2$ while $H^2$ shrinks to a point. Here we also consider Yang-Mills theory on a three-dimensional manifold $\Sigma_2\times S^1$ and show that in the limit when the radius of $S^1$ tends to zero, the Yang-Mills action functional supplemented by a Wess-Zumino-type term becomes the Green-Schwarz superstring action.Comment: 11 pages, v3: clarifying remarks added, new section on embedding of the Green-Schwarz superstring into d=3 Yang-Mills theory include

Birkhoff strata of the Grassmannian Gr(2)\mathrm{^{(2)}}: Algebraic curves

Algebraic varieties and curves arising in Birkhoff strata of the Sato Grassmannian Gr${^{(2)}}$ are studied. It is shown that the big cell $\Sigma_0$ contains the tower of families of the normal rational curves of all odd orders. Strata $\Sigma_{2n}$, $n=1,2,3,...$ contain hyperelliptic curves of genus $n$ and their coordinate rings. Strata $\Sigma_{2n+1}$, $n=0,1,2,3,...$ contain $(2m+1,2m+3)-$plane curves for $n=2m,2m-1$ $(m \geq 2)$ and $(3,4)$ and $(3,5)$ curves in $\Sigma_3$, $\Sigma_5$ respectively. Curves in the strata $\Sigma_{2n+1}$ have zero genus.Comment: 14 pages, no figures, improved some definitions, typos correcte

Tissue specific membrane association of α1T, a truncated form of the α1 subunit of the Na pump

AbstractWe have assessed the Na pump α-subunit isoform content utilizing site directed antibodies in two vascular smooth muscle (VSM) preparations known to contain functional Na pump sites, VSM microsomal fractions (Na+,K+-ATPase) and intact primary confluent cells (ouabain inhibited 86Rb uptake). A comparison of isoform content was made with kidney microsomes. Both VSM and kidney microsomes contained a full length α1 subunit (~100 kDa) as well as a truncated subunit, α1T (~66 kDa). SDS treatment of VSM microsomes effected an increase in Na+,K+-ATPase and a retention of α1T. SDS treated kidney microsomes retained the α1 isoform and Na+,K+-ATPase. Confluent VSM cells showed no detectable α1T, only α1T. In the absence of detectable full length α1, the α1T protein may represent a functional Na pump component in canine VSM

Social Support and Survival Strategies of Older African American Grandmother Caregivers

The effects of caring for grandchildren on grandparents’ emotional and physical well-being have become a significant area of focus in behavioral and medical research. Research suggests that African American grandmothers may experience increased mental and physical health challenges due to their caregiving stressors. To buffer the adverse influence of stress, caregivers often rely on informal social support from family and/or community members. In this study we explored older, African American caregivers’ management of their emotional well-being within the context and circumstances of available to minimal social support from family and community. During an 18-month period, seven caregiving grandmothers participated in three face-to-face, audiotaped, semi-structured interviews; eco-map and genogram data was included to understand the contextual complexities of caregivers’ social support and their strategies for survival. Using constant comparative analysis, six interrelated themes revealed grandmothers operated along a continuum of reliable to unreliable social support. In the context of these varying ranges of social support, four sub-themes depicting their survival strategies were identified: being strong, self-sacrificing, receiving help and self-compassion. Utilization of each survival strategy was dependent on grandmothers’ perception of where they fell on the continuum of reliable to unreliable social support. Grandmothers who engaged in being strong and self-sacrificing engaged in stress-related health behaviors, such as emotional eating, smoking nicotine, disruptive sleep patterns and postponement of self-care. We offer specific practice recommendations for addressing the emotional and physical health needs of grandmother caregivers