Exact results for N = 2 supersymmetric gauge theories on compact toric manifolds and equivariant Donaldson invariants

We provide a contour integral formula for the exact partition function of N = 2 supersymmetric U(N) gauge theories on compact toric four-manifolds by means of supersymmetric localisation. We perform the explicit evaluation of the contour integral for U(2) N = 2 17 theory on CP2 for all instanton numbers. In the zero mass case, corresponding to the N = 4 supersymmetric gauge theory, we obtain the generating function of the Euler characteristics of instanton moduli spaces in terms of mock-modular forms. In the decoupling limit of infinite mass we find that the generating function of local and surface observables computes equivariant Donaldson invariants, thus proving in this case a longstanding conjecture by N. Nekrasov. In the case of vanishing first Chern class the resulting equivariant Donaldson polynomials are new. \ua9 2016, The Author(s)

Exact Results in D=2 Supersymmetric Gauge Theories

We compute exactly the partition function of two dimensional N=(2,2) gauge theories on S^2 and show that it admits two dual descriptions: either as an integral over the Coulomb branch or as a sum over vortex and anti-vortex excitations on the Higgs branches of the theory. We further demonstrate that correlation functions in two dimensional Liouville/Toda CFT compute the S^2 partition function for a class of N=(2,2) gauge theories, thereby uncovering novel modular properties in two dimensional gauge theories. Some of these gauge theories flow in the infrared to Calabi-Yau sigma models - such as the conifold - and the topology changing flop transition is realized as crossing symmetry in Liouville/Toda CFT. Evidence for Seiberg duality in two dimensions is exhibited by demonstrating that the partition function of conjectured Seiberg dual pairs are the same.Comment: 78 pages, LaTeX; v2: small corrections and references added; v3: JHEP version, discussing factorization further in new appendix F; v4: sign corrected for non simply-connected gauge grou

Six-dimensional supersymmetric gauge theories, quantum cohomology of instanton moduli spaces and gl(N) Quantum Intermediate Long Wave Hydrodynamics

We show that the exact partition function of U(N) six-dimensional gauge theory with eight supercharges on \u21022 7 S 2 provides the quantization of the integrable system of hydrodynamic type known as gl(N) periodic Intermediate Long Wave (ILW). We characterize this system as the hydrodynamic limit of elliptic Calogero-Moser integrable system. We compute the Bethe equations from the effective gauged linear sigma model on S 2 with target space the ADHM instanton moduli space, whose mirror computes the Yang-Yang function of gl(N) ILW. The quantum Hamiltonians are given by the local chiral ring observables of the six-dimensional gauge theory. As particular cases, these provide the gl(N) Benjamin-Ono and Korteweg-de Vries quantum Hamiltonians. In the four dimensional limit, we identify the local chiral ring observables with the conserved charges of Heisenberg plus W N algebrae, thus providing a gauge theoretical proof of AGT correspondence. \ua9 2014 The Author(s)

Huntington's disease: a clinical review

Huntington disease (HD) is a rare neurodegenerative disorder of the central nervous system characterized by unwanted choreatic movements, behavioral and psychiatric disturbances and dementia. Prevalence in the Caucasian population is estimated at 1/10,000-1/20,000. Mean age at onset of symptoms is 30-50 years. In some cases symptoms start before the age of 20 years with behavior disturbances and learning difficulties at school (Juvenile Huntington's disease; JHD). The classic sign is chorea that gradually spreads to all muscles. All psychomotor processes become severely retarded. Patients experience psychiatric symptoms and cognitive decline. HD is an autosomal dominant inherited disease caused by an elongated CAG repeat (36 repeats or more) on the short arm of chromosome 4p16.3 in the Huntingtine gene. The longer the CAG repeat, the earlier the onset of disease. In cases of JHD the repeat often exceeds 55. Diagnosis is based on clinical symptoms and signs in an individual with a parent with proven HD, and is confirmed by DNA determination. Pre-manifest diagnosis should only be performed by multidisciplinary teams in healthy at-risk adult individuals who want to know whether they carry the mutation or not. Differential diagnoses include other causes of chorea including general internal disorders or iatrogenic disorders. Phenocopies (clinically diagnosed cases of HD without the genetic mutation) are observed. Prenatal diagnosis is possible by chorionic villus sampling or amniocentesis. Preimplantation diagnosis with in vitro fertilization is offered in several countries. There is no cure. Management should be multidisciplinary and is based on treating symptoms with a view to improving quality of life. Chorea is treated with dopamine receptor blocking or depleting agents. Medication and non-medical care for depression and aggressive behavior may be required. The progression of the disease leads to a complete dependency in daily life, which results in patients requiring full-time care, and finally death. The most common cause of death is pneumonia, followed by suicide

The ABCDEFG of Instantons and W-algebras

For arbitrary gauge groups, we check at the one-instanton level that the Nekrasov partition function of pure N=2 super Yang-Mills is equal to the norm of a certain coherent state of the corresponding W-algebra. For non-simply-laced gauge groups, we confirm in particular that the coherent state is in the twisted sector of a simply-laced W-algebra.Comment: 30 pages, 2 figures, v2: references added, explicit expression for the W(E6) generators adde

Conserved genes and pathways in primary human fibroblast strains undergoing replicative and radiation induced senescence

Additional file 3: Figure S3. Regulation of genes of Arrhythmogenic right ventricular cardiomyopathy pathway during senescence induction in HFF strains Genes of the “Arrhythmogenic right ventricular cardiomyopathy” pathway which are significantly up- (green) and down- (red) regulated (log2 fold change >1) during irradiation induced senescence (120 h after 20 Gy irradiation) in HFF strains. Orange color signifies genes which are commonly up-regulated during both, irradiation induced and replicative senescence

All-sky search for gravitational-wave bursts in the second joint LIGO-Virgo run

We present results from a search for gravitational-wave bursts in the data collected by the LIGO and Virgo detectors between July 7, 2009 and October 20, 2010: data are analyzed when at least two of the three LIGO-Virgo detectors are in coincident operation, with a total observation time of 207 days. The analysis searches for transients of duration < 1 s over the frequency band 64-5000 Hz, without other assumptions on the signal waveform, polarization, direction or occurrence time. All identified events are consistent with the expected accidental background. We set frequentist upper limits on the rate of gravitational-wave bursts by combining this search with the previous LIGO-Virgo search on the data collected between November 2005 and October 2007. The upper limit on the rate of strong gravitational-wave bursts at the Earth is 1.3 events per year at 90% confidence. We also present upper limits on source rate density per year and Mpc^3 for sample populations of standard-candle sources. As in the previous joint run, typical sensitivities of the search in terms of the root-sum-squared strain amplitude for these waveforms lie in the range 5 10^-22 Hz^-1/2 to 1 10^-20 Hz^-1/2. The combination of the two joint runs entails the most sensitive all-sky search for generic gravitational-wave bursts and synthesizes the results achieved by the initial generation of interferometric detectors.Comment: 15 pages, 7 figures: data for plots and archived public version at https://dcc.ligo.org/cgi-bin/DocDB/ShowDocument?docid=70814&version=19, see also the public announcement at http://www.ligo.org/science/Publication-S6BurstAllSky