Large N reduction on group manifolds

We show that the large N reduction holds on group manifolds. Large N field theories defined on group manifolds are equivalent to some corresponding matrix models. For instance, gauge theories on S^3 can be regularized in a gauge invariant and SO(4) invariant manner.Comment: 21 pages, 4 figures, typos corrected, a reference adde

Embedding of theories with SU(2|4) symmetry into the plane wave matrix model

We study theories with SU(2|4) symmetry, which include the plane wave matrix model, 2+1 SYM on RxS^2 and N=4 SYM on RxS^3/Z_k. All these theories possess many vacua. From Lin-Maldacena's method which gives the gravity dual of each vacuum, it is predicted that the theory around each vacuum of 2+1 SYM on RxS^2 and N=4 SYM on RxS^3/Z_k is embedded in the plane wave matrix model. We show this directly on the gauge theory side. We clearly reveal relationships among the spherical harmonics on S^3, the monopole harmonics and the harmonics on fuzzy spheres. We extend the compactification (the T-duality) in matrix models a la Taylor to that on spheres.Comment: 56 pages, 6 figures, v2:a footnote and references added, section 5.2 improved, typos corrected, v3:typos corrected, v4: some equations are corrected, eq.(G.2) is added, conclusion is unchange

N=4 Super Yang-Mills from the Plane Wave Matrix Model

We propose a nonperturbative definition of N=4 super Yang-Mills (SYM). We realize N=4 SYM on RxS^3 as the theory around a vacuum of the plane wave matrix model. Our regularization preserves sixteen supersymmetries and the gauge symmetry. We perform the 1-loop calculation to give evidences that the superconformal symmetry is restored in the continuum limit.Comment: 39 pages, 6 figures, some sentences are improved, references added, typos corrected, version to appear in PR

Complex Matrix Model and Fermion Phase Space for Bubbling AdS Geometries

We study a relation between droplet configurations in the bubbling AdS geometries and a complex matrix model that describes the dynamics of a class of chiral primary operators in dual N=4 super Yang Mills (SYM). We show rigorously that a singlet holomorphic sector of the complex matrix model is equivalent to a holomorphic part of two-dimensional free fermions, and establish an exact correspondence between the singlet holomorphic sector of the complex matrix model and one-dimensional free fermions. Based on this correspondence, we find a relation of the singlet holomorphic operators of the complex matrix model to the Wigner phase space distribution. By using this relation and the AdS/CFT duality, we give a further evidence that the droplets in the bubbling AdS geometries are identified with those in the phase space of the one-dimensional fermions. We also show that the above correspondence actually maps the operators of N=4 SYM corresponding to the (dual) giant gravitons to the droplet configurations proposed in the literature.Comment: 27 pages, 6 figures, some clarification, typos corrected, published versio

Testing a novel large-N reduction for N=4 super Yang-Mills theory on RxS^3

Recently a novel large-N reduction has been proposed as a maximally supersymmetric regularization of N=4 super Yang-Mills theory on RxS^3 in the planar limit. This proposal, if it works, will enable us to study the theory non-perturbatively on a computer, and hence to test the AdS/CFT correspondence analogously to the recent works on the D0-brane system. We provide a nontrivial check of this proposal by performing explicit calculations in the large-N reduced model, which is nothing but the so-called plane wave matrix model, around a particular stable vacuum corresponding to RxS^3. At finite temperature and at weak coupling, we reproduce precisely the deconfinement phase transition in the N=4 super Yang-Mills theory on RxS^3. This phase transition is considered to continue to the strongly coupled regime, where it corresponds to the Hawking-Page transition on the AdS side. We also perform calculations around other stable vacua, and reproduce the phase transition in super Yang-Mills theory on the corresponding curved space-times such as RxS^3/Z_q and RxS^2.Comment: 24 pages, 4 figure

Delivery of epilepsy care to adults with intellectual and developmental disabilities

Epilepsy is common in people with intellectual and developmental disabilities (IDD). In adulthood, patients with IDD and epilepsy (IDD-E) have neurologic, psychiatric, medical, and social challenges compounded by fragmented and limited care. With increasing neurologic disability, there is a higher frequency of epilepsy, especially symptomatic generalized and treatment-resistant epilepsies. The causes of IDD-E are increasingly recognized to be genetic based on chromosomal microarray analysis to identify copy number variants, gene panels (epilepsy, autism spectrum disorder, intellectual disability), and whole-exome sequencing. A specific genetic diagnosis may guide care by pointing to comorbid disorders and best therapy. Therapy to control seizures should be individualized, with drug selection based on seizure types, epilepsy syndrome, concomitant medications, and comorbid disorders. There are limited comparative antiepileptic drug data in the IDD-E population. Vagus nerve and responsive neural stimulation therapies and resective surgery should be considered. Among the many comorbid disorders that affect patients with IDD-E, psychiatric and sleep disorders are common but often unrecognized and typically not treated. Transition from holistic and coordinated pediatric to adult care is often a vulnerable period. Communication among adult health care providers is complex but essential to ensure best care when these patients are seen in outpatient, emergency room, and inpatient settings. We propose specific recommendations for minimum care standards for people with IDD-E

Nasal tip reconstruction: case reports and historical review

Traumatic amputations of the nasal tip are disfiguring injuries, which determine important social rejection, imposing additional suffering on the patient and those already caused by the wound and its functional limitations resulting from the trauma. Such defects represent a challenge for plastic surgeons, and several techniques can be adopted to treat this type of defect. This work shows three cases of traumatic amputation exclusively of the nasal tip with their respective treatments. They present a historical review and discussion of the different techniques used for nasal tip reconstruction, comparatively evaluating and emphasizing the technical evolution in plastic surgery armament