Vortices, Instantons and Branes

The purpose of this paper is to describe a relationship between the moduli space of vortices and the moduli space of instantons. We study charge k vortices in U(N) Yang-Mills-Higgs theories and show that the moduli space is isomorphic to a special Lagrangian submanifold of the moduli space of k instantons in non-commutative U(N) Yang-Mills theories. This submanifold is the fixed point set of a U(1) action on the instanton moduli space which rotates the instantons in a plane. To derive this relationship, we present a D-brane construction in which the dynamics of vortices is described by the Higgs branch of a U(k) gauge theory with 4 supercharges which is a truncation of the familiar ADHM gauge theory. We further describe a moduli space construction for semi-local vortices, lumps in the CP(N) and Grassmannian sigma-models, and vortices on the non-commutative plane. We argue that this relationship between vortices and instantons underlies many of the quantitative similarities shared by quantum field theories in two and four dimensions.Comment: 32 Pages, 4 Figure

Nonrigid chiral soliton for the octet and decuplet baryons

Systematic treatment of the collective rotation of the nonrigid chiral soliton is developed in the SU(3) chiral quark soliton model and applied to the octet and decuplet baryons. The strangeness degrees of freedom are treated by a simplified bound-state approach which omits the locality of the kaon wave function. Then, the flavor rotation is divided into the isospin rotation and the emission and absorption of the kaon. The kaon Hamiltonian is diagonalized by the Hartree approximation. The soliton changes the shape according to the strangeness. The baryons appear as the rotational bands of the combined system of the soliton and the kaon.Comment: 11 pages(LaTex), 1 figures(eps

Superconformal operators in N=4 super-Yang-Mills theory

We construct, in the framework of the N=4 SYM theory, a supermultiplet of twist-two conformal operators and study their renormalization properties. The components of the supermultiplet have the same anomalous dimension and enter as building blocks into multi-particle quasipartonic operators. The latter are determined by the condition that their twist equals the number of elementary constituent fields from which they are built. A unique feature of the N=4 SYM is that all quasipartonic operators with different SU(4) quantum numbers fall into a single supermultiplet. Among them there is a subsector of the operators of maximal helicity, which has been known to be integrable in the multi-color limit in QCD, independent of the presence of supersymmetry. In the N=4 SYM theory, this symmetry is extended to the whole supermultiplet of quasipartonic operators and the one-loop dilatation operator coincides with a Hamiltonian of integrable SL(2|4) Heisenberg spin chain.Comment: 45 pages, Latex, 4 figure

Spontaneous Chiral-Symmetry Breaking in Three-Dimensional QED with a Chern--Simons Term

In three-dimensional QED with a Chern--Simons term we study the phase structure associated with chiral-symmetry breaking in the framework of the Schwinger--Dyson equation. We give detailed analyses on the analytical and numerical solutions for the Schwinger--Dyson equation of the fermion propagator, where the nonlocal gauge-fixing procedure is adopted to avoid wave-function renormalization for the fermion. In the absence of the Chern--Simons term, there exists a finite critical number of four-component fermion flavors, at which a continuous (infinite-order) chiral phase transition takes place and below which the chiral symmetry is spontaneously broken. In the presence of the Chern--Simons term, we find that the spontaneous chiral-symmetry-breaking transition continues to exist, but the type of phase transition turns into a discontinuous first-order transition. A simple stability argument is given based on the effective potential, whose stationary point gives the solution of the Schwinger-Dyson equation.Comment: 34 pages, revtex, with 9 postscriptfigures appended (uuencoded

The fuzzy S^2 structure of M2-M5 systems in ABJM membrane theories

We analyse the fluctuations of the ground-state/funnel solutions proposed to describe M2-M5 systems in the level-k mass-deformed/pure Chern-Simons-matter ABJM theory of multiple membranes. We show that in the large N limit the fluctuations approach the space of functions on the 2-sphere rather than the naively expected 3-sphere. This is a novel realisation of the fuzzy 2-sphere in the context of Matrix Theories, which uses bifundamental instead of adjoint scalars. Starting from the multiple M2-brane action, a U(1) Yang-Mills theory on R^{2,1} x S^2 is recovered at large N, which is consistent with a single D4-brane interpretation in Type IIA string theory. This is as expected at large k, where the semiclassical analysis is valid. Several aspects of the fluctuation analysis, the ground-state/funnel solutions and the mass-deformed/pure ABJM equations can be understood in terms of a discrete noncommutative realisation of the Hopf fibration. We discuss the implications for the possibility of finding an M2-brane worldvolume derivation of the classical S^3 geometry of the M2-M5 system. Using a rewriting of the equations of the SO(4)-covariant fuzzy 3-sphere construction, we also directly compare this fuzzy 3-sphere against the ABJM ground-state/funnel solutions and show them to be different.Comment: 60 pages, Latex; v2: references added; v3: typos corrected and references adde

Effects of rare kidney diseases on kidney failure: a longitudinal analysis of the UK National Registry of Rare Kidney Diseases (RaDaR) cohort

Background Individuals with rare kidney diseases account for 5–10% of people with chronic kidney disease, but constitute more than 25% of patients receiving kidney replacement therapy. The National Registry of Rare Kidney Diseases (RaDaR) gathers longitudinal data from patients with these conditions, which we used to study disease progression and outcomes of death and kidney failure. Methods People aged 0–96 years living with 28 types of rare kidney diseases were recruited from 108 UK renal care facilities. The primary outcomes were cumulative incidence of mortality and kidney failure in individuals with rare kidney diseases, which were calculated and compared with that of unselected patients with chronic kidney disease. Cumulative incidence and Kaplan–Meier survival estimates were calculated for the following outcomes: median age at kidney failure; median age at death; time from start of dialysis to death; and time from diagnosis to estimated glomerular filtration rate (eGFR) thresholds, allowing calculation of time from last eGFR of 75 mL/min per 1·73 m2 or more to first eGFR of less than 30 mL/min per 1·73 m2 (the therapeutic trial window). Findings Between Jan 18, 2010, and July 25, 2022, 27 285 participants were recruited to RaDaR. Median follow-up time from diagnosis was 9·6 years (IQR 5·9–16·7). RaDaR participants had significantly higher 5-year cumulative incidence of kidney failure than 2·81 million UK patients with all-cause chronic kidney disease (28% vs 1%; p<0·0001), but better survival rates (standardised mortality ratio 0·42 [95% CI 0·32–0·52]; p<0·0001). Median age at kidney failure, median age at death, time from start of dialysis to death, time from diagnosis to eGFR thresholds, and therapeutic trial window all varied substantially between rare diseases. Interpretation Patients with rare kidney diseases differ from the general population of individuals with chronic kidney disease: they have higher 5-year rates of kidney failure but higher survival than other patients with chronic kidney disease stages 3–5, and so are over-represented in the cohort of patients requiring kidney replacement therapy. Addressing unmet therapeutic need for patients with rare kidney diseases could have a large beneficial effect on long-term kidney replacement therapy demand. Funding RaDaR is funded by the Medical Research Council, Kidney Research UK, Kidney Care UK, and the Polycystic Kidney Disease Charity

Effects of rare kidney diseases on kidney failure: a longitudinal analysis of the UK National Registry of Rare Kidney Diseases (RaDaR) cohort

Background Individuals with rare kidney diseases account for 5–10% of people with chronic kidney disease, but constitute more than 25% of patients receiving kidney replacement therapy. The National Registry of Rare Kidney Diseases (RaDaR) gathers longitudinal data from patients with these conditions, which we used to study disease progression and outcomes of death and kidney failure. Methods People aged 0–96 years living with 28 types of rare kidney diseases were recruited from 108 UK renal care facilities. The primary outcomes were cumulative incidence of mortality and kidney failure in individuals with rare kidney diseases, which were calculated and compared with that of unselected patients with chronic kidney disease. Cumulative incidence and Kaplan–Meier survival estimates were calculated for the following outcomes: median age at kidney failure; median age at death; time from start of dialysis to death; and time from diagnosis to estimated glomerular filtration rate (eGFR) thresholds, allowing calculation of time from last eGFR of 75 mL/min per 1·73 m2 or more to first eGFR of less than 30 mL/min per 1·73 m2 (the therapeutic trial window). Findings Between Jan 18, 2010, and July 25, 2022, 27 285 participants were recruited to RaDaR. Median follow-up time from diagnosis was 9·6 years (IQR 5·9–16·7). RaDaR participants had significantly higher 5-year cumulative incidence of kidney failure than 2·81 million UK patients with all-cause chronic kidney disease (28% vs 1%; p<0·0001), but better survival rates (standardised mortality ratio 0·42 [95% CI 0·32–0·52]; p<0·0001). Median age at kidney failure, median age at death, time from start of dialysis to death, time from diagnosis to eGFR thresholds, and therapeutic trial window all varied substantially between rare diseases. Interpretation Patients with rare kidney diseases differ from the general population of individuals with chronic kidney disease: they have higher 5-year rates of kidney failure but higher survival than other patients with chronic kidney disease stages 3–5, and so are over-represented in the cohort of patients requiring kidney replacement therapy. Addressing unmet therapeutic need for patients with rare kidney diseases could have a large beneficial effect on long-term kidney replacement therapy demand