The Ruijsenaars-Schneider Model in the Context of Seiberg-Witten Theory

The compactification of five dimensional N=2 SUSY Yang-Mills (YM) theory onto a circle provides a four dimensional YM model with N=4 SUSY. This supersymmetry can be broken down to N=2 if non-trivial boundary conditions in the compact dimension, \phi(x_5 +R) = e^{2\pi i\epsilon}\phi(x_5), are imposed on half of the fields. This two-parameter (R,\epsilon) family of compactifications includes as particular limits most of the previously studied four dimensional N=2 SUSY YM models with supermultiplets in the adjoint representation of the gauge group. The finite-dimensional integrable system associated to these theories via the Seiberg-Witten construction is the generic elliptic Ruijsenaars-Schneider model. In particular the perturbative (weak coupling) limit is described by the trigonometric Ruijsenaars-Schneider model.Comment: 18 pages, LaTe

From dynamical scaling to local scale-invariance: a tutorial

Dynamical scaling arises naturally in various many-body systems far from equilibrium. After a short historical overview, the elements of possible extensions of dynamical scaling to a local scale-invariance will be introduced. Schr\"odinger-invariance, the most simple example of local scale-invariance, will be introduced as a dynamical symmetry in the Edwards-Wilkinson universality class of interface growth. The Lie algebra construction, its representations and the Bargman superselection rules will be combined with non-equilibrium Janssen-de Dominicis field-theory to produce explicit predictions for responses and correlators, which can be compared to the results of explicit model studies. At the next level, the study of non-stationary states requires to go over, from Schr\"odinger-invariance, to ageing-invariance. The ageing algebra admits new representations, which acts as dynamical symmetries on more general equations, and imply that each non-equilibrium scaling operator is characterised by two distinct, independent scaling dimensions. Tests of ageing-invariance are described, in the Glauber-Ising and spherical models of a phase-ordering ferromagnet and the Arcetri model of interface growth.Comment: 1+ 23 pages, 2 figures, final for

BGWM as Second Constituent of Complex Matrix Model

Earlier we explained that partition functions of various matrix models can be constructed from that of the cubic Kontsevich model, which, therefore, becomes a basic elementary building block in "M-theory" of matrix models. However, the less topical complex matrix model appeared to be an exception: its decomposition involved not only the Kontsevich tau-function but also another constituent, which we now identify as the Brezin-Gross-Witten (BGW) partition function. The BGW tau-function can be represented either as a generating function of all unitary-matrix integrals or as a Kontsevich-Penner model with potential 1/X (instead of X^3 in the cubic Kontsevich model).Comment: 42 page

CRISPR/Cas9 editing to generate a heterozygous COL2A1 p.G1170S human chondrodysplasia iPSC line, MCRIi019-A-2, in a control iPSC line, MCRIi019-A

© 2020 To develop an in vitro disease model of a human chondrodysplasia, we used CRISPR/Cas9 gene editing to generate a heterozygous COL2A1 exon 50 c.3508 GGT > TCA (p.G1170S) mutation in a control human iPSC line. Both the control and COL2A1 mutant lines displayed typical iPSC characteristics, including normal cell morphology, expression of pluripotency markers, the ability to differentiate into endoderm, ectoderm and mesoderm lineages and normal karyotype. These chondrodysplasia mutant and isogenic control cell lines can be used to explore disease mechanisms underlying type II collagenopathies and aid in the discovery of new therapeutic strategies