Schizophrenia and the progression of emotional expression in relation to others

Gaining an improved understanding of people diagnosed with schizophrenia has the potential to influence priorities for therapy. Psychosis is commonly understood through the perspective of the medical model. However, the experience of social context surrounding psychosis is not well understood. In this research project we used a phenomenological methodology with a longitudinal design to interview 7 participants across a 12-month period to understand the social experiences surrounding psychosis. Eleven themes were explicated and divided into two phases of the illness experience: (a) transition into emotional shutdown included the experiences of not being acknowledged, relational confusion, not being expressive, detachment, reliving the past, and having no sense of direction; and (b) recovery from emotional shutdown included the experiences of being acknowledged, expression, resolution, independence, and a sense of direction. The experiential themes provide clinicians with new insights to better assess vulnerability, and have the potential to inform goals for therapy

The Grassmannian and the Twistor String: Connecting All Trees in N=4 SYM

We present a new, explicit formula for all tree-level amplitudes in N=4 super Yang-Mills. The formula is written as a certain contour integral of the connected prescription of Witten's twistor string, expressed in link variables. A very simple deformation of the integrand gives directly the Grassmannian integrand proposed by Arkani-Hamed et al. together with the explicit contour of integration. The integral is derived by iteratively adding particles to the Grassmannian integral, one particle at a time, and makes manifest both parity and soft limits. The formula is shown to be related to those given by Dolan and Goddard, and generalizes the results of earlier work for NMHV and N^2MHV to all N^(k-2)MHV tree amplitudes in N=4 super Yang-Mills.Comment: 26 page

Some analytic results for two-loop scattering amplitudes

We present analytic results for the finite diagrams contributing to the two-loop eight-point MHV scattering amplitude of planar N=4 SYM. We use a recently proposed representation for the integrand of the amplitude in terms of (momentum) twistors and focus on a restricted kinematics in which the answer depends only on two independent cross-ratios. The theory of motives can be used to vastly simplify the results, which can be expressed as simple combinations of classical polylogarithms.Comment: 18 page

On the Classification of Residues of the Grassmannian

We study leading singularities of scattering amplitudes which are obtained as residues of an integral over a Grassmannian manifold. We recursively do the transformation from twistors to momentum twistors and obtain an iterative formula for Yangian invariants that involves a succession of dualized twistor variables. This turns out to be useful in addressing the problem of classifying the residues of the Grassmannian. The iterative formula leads naturally to new coordinates on the Grassmannian in terms of which both composite and non-composite residues appear on an equal footing. We write down residue theorems in these new variables and classify the independent residues for some simple examples. These variables also explicitly exhibit the distinct solutions one expects to find for a given set of vanishing minors from Schubert calculus.Comment: 20 page

The super-correlator/super-amplitude duality: Part I

We extend the recently discovered duality between MHV amplitudes and the light-cone limit of correlation functions of a particular type of local scalar operators to generic non-MHV amplitudes in planar N=4 SYM theory. We consider the natural generalization of the bosonic correlators to super-correlators of stress-tensor multiplets and show, in a number of examples, that their light-cone limit exactly reproduces the square of the matching super-amplitudes. Our correlators are computed at Born level. If all of their points form a light-like polygon, the correlator is dual to the tree-level amplitude. If a subset of points are not on the polygon but are integrated over, they become Lagrangian insertions generating the loop corrections to the correlator. In this case the duality with amplitudes holds at the level of the integrand. We build up the superspace formalism needed to formulate the duality and present the explicit example of the n-point NMHV tree amplitude as the dual of the lowest nilpotent level in the correlator.Comment: 56 page

Dual conformal constraints and infrared equations from global residue theorems in N=4 SYM theory

Infrared equations and dual conformal constraints arise as consistency conditions on loop amplitudes in N=4 super Yang-Mills theory. These conditions are linear relations between leading singularities, which can be computed in the Grassmannian formulation of N=4 super Yang-Mills theory proposed recently. Examples for infrared equations have been shown to be implied by global residue theorems in the Grassmannian picture. Both dual conformal constraints and infrared equations are mapped explicitly to global residue theorems for one-loop next-to-maximally-helicity-violating amplitudes. In addition, the identity relating the BCFW and its parity-conjugated form of tree-level amplitudes, is shown to emerge from a particular combination of global residue theorems.Comment: 21 page

On All-loop Integrands of Scattering Amplitudes in Planar N=4 SYM

We study the relationship between the momentum twistor MHV vertex expansion of planar amplitudes in N=4 super-Yang-Mills and the all-loop generalization of the BCFW recursion relations. We demonstrate explicitly in several examples that the MHV vertex expressions for tree-level amplitudes and loop integrands satisfy the recursion relations. Furthermore, we introduce a rewriting of the MHV expansion in terms of sums over non-crossing partitions and show that this cyclically invariant formula satisfies the recursion relations for all numbers of legs and all loop orders.Comment: 34 pages, 17 figures; v2: Minor improvements to exposition and discussion, updated references, typos fixe

Argyres–Douglas theories, S 1 reductions, and topological symmetries

journal_title: Journal of Physics A: Mathematical and Theoretical article_type: paper article_title: Argyres–Douglas theories, reductions, and topological symmetries copyright_information: © 2016 IOP Publishing Ltd license_information: cc-by Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. date_received: 2015-07-22 date_accepted: 2015-10-29 date_epub: 2015-12-21journal_title: Journal of Physics A: Mathematical and Theoretical article_type: paper article_title: Argyres–Douglas theories, reductions, and topological symmetries copyright_information: © 2016 IOP Publishing Ltd license_information: cc-by Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. date_received: 2015-07-22 date_accepted: 2015-10-29 date_epub: 2015-12-21Our research is partially supported by the U S Department of Energy under grants DOE-SC0010008, DOE-ARRA-SC0003883, and DOE-DE-SC0007897