Wilson loops in unitary matrix models at finite NN

It is known that the expectation value of Wilson loops in the Gross-Witten-Wadia (GWW) unitary matrix model can be computed exactly at finite $N$ for arbitrary representations. We study the perturbative and non-perturbative corrections of Wilson loops in the $1/N$ expansion, either analytically or numerically using the exact result at finite $N$. As a by-product of the exact result of Wilson loops, we propose a large $N$ master field of GWW model. This master field has an interesting eigenvalue distribution. We also study the Wilson loops in large representations, called Giant Wilson loops, and comment on the Hagedorn/deconfinement transition of a unitary matrix model with a double trace interaction.Comment: 38 page

Instanton Corrections of 1/6 BPS Wilson Loops in ABJM Theory

We study instanton corrections to the vacuum expectation value (VEV) of 1/6 BPS Wilson loops in ABJM theory from the Fermi gas approach. We mainly consider Wilson loops in the fundamental representation and winding Wilson loops, but we also initiate the study of Wilson loops with two boundaries. We find that the membrane instanton corrections to the Wilson loop VEV are determined by the refined topological string in the Nekrasov-Shatashvili limit, and the pole cancellation mechanism between membrane instantons and worldsheet instantons works also in the Wilson loop VEVs as in the case of the partition functions.Comment: 40 pages, 12 figure

An Investigation of Successful and Unsuccessful Communication between International and North African Social Workers at Centres for Disabled Children in North Africa

There is a need to improve the quality of life for disabled children in North Africa. Although local governments and communities have been providing social services support, an increase in social services investment, particularly, specialists who work in the area of providing disability support, is needed from local and international organisations. However, international social workers’ lack of cross cultural sensitivity creates communication barriers and prevents effective means of collaboration between international and local social workers. The main aim of this research is to identify culturally appropriate communication skills and possible pitfalls for international social workers by investigating successful and unsuccessful communication between international and local social workers working at schools and centres for disabled children in North Africa. A constructivist qualitative approach has been used to explore the complex world of lived experiences of the social workers. The stories of four international and three local social workers were gathered through semi structured in-depth interviews. Three main themes emerged as a result of analysis of the interviews: language and religious value, gender relations, shame and honour. The findings have shown that in order for international social workers to communicate culturally appropriately and achieve successful collaboration with local social workers, the international workers need to be aware of the differences in mind-sets between individualistic and collective cultures, and be sensitive to the Arab/ Muslim cultural values of local social workers

Adelic equidistribution, characterization of equidistribution, and a general equidistribution theorem in non-archimedean dynamics

We determine when the equidistribution property for possibly moving targets holds for a rational function of degree more than one on the projective line over an algebraically closed field of any characteristic and complete with respect to a non-trivial absolute value. This characterization could be useful in the positive characteristic case. Based on the variational argument, we give a purely local proof of the adelic equidistribution theorem for possibly moving targets, which is due to Favre and Rivera-Letelier, using a dynamical Diophantine approximation theorem by Silverman and by Szpiro--Tucker. We also give a proof of a general equidistribution theorem for possibly moving targets, which is due to Lyubich in the archimedean case and due to Favre and Rivera-Letelier for constant targets in the non-archimedean and any characteristic case and for moving targets in the non-archimedean and 0 characteristic case.Comment: 25 pages, no figures. (v2: a few minor modifications

Probing non-perturbative effects in M-theory on orientifolds

Using holography, we study non-perturbative effects in M-theory on orientifolds from the analysis of the S^3 partition functions of dual field theories. We consider the S^3 partition functions of N=4 Yang-Mills theory with O(n) gauge symmetry coupled to one (anti)symmetric and N_f fundamental hypermultiplets from the Fermi gas approach. In addition to the worldsheet instanton and membrane instanton corrections to the grand potential, which are also present in the U(n) Yang-Mills case, we find that there exist "half instanton" corrections coming from the effect of orientifold plane.Comment: 31 pages, 7 figure