A Fourier transform for sheaves on Lagrangian families of real tori

We systematically develop a transform of the Fourier-Mukai type for sheaves on symplectic manifolds $X$ of any dimension fibred in Lagrangian tori. One obtains a bijective correspondence between unitary local systems supported on Lagrangian submanifolds of $X$ and holomorphic vector bundles with compatible unitary connections supported on complex submanifolds of the relative Jacobian of $X$ (suitable conditions being verified on both sides).Comment: Latex, 30 pages (in a4wide format), no figures. v2: Minor expository changes, typos corrected. v3: Final version to appear in two parts in J. Geom. Phy

Superlocalization formulas and supersymmetric Yang-Mills theories

By using supermanifold techniques we prove a generalization of the localization formula in equivariant cohomology which is suitable for studying supersymmetric Yang-Mills theories in terms of ADHM data. With these techniques one can compute the reduced partition functions of topological super Yang-Mills theory with 4, 8 or 16 supercharges. More generally, the superlocalization formula can be applied to any topological field theory in any number of dimensions.Comment: 22 pages, Latex2

Complex Lagrangian embeddings of moduli spaces of vector bundles

By means of a Fourier-Mukai transform we embed moduli spaces of stable bundles on an algebraic curve C as isotropic subvarieties of moduli spaces of mu-stable bundles on the Jacobian variety J(C). When g(C)=2 this provides new examples of special Lagrangian submanifolds.Comment: 9 pages, no figures, to appear in Diff. Geom. App

Multi instanton tests of holography

Gauge theories living on stacks of D7-branes are holographically related to IIB gravitational backgrounds with a varying axion-dilaton field (F-theory). The axion-dilaton field is generated by D7, O7 and D-instanton sources and can be written in terms of the chiral correlators of the eight dimensional gauge theory living on the D7-branes. Using localization techniques, we prove that the same correlators determine the gauge coupling of the four-dimensional N=2 supersymmetric SU(2) gauge theories living on the elementary D3-brane which probes the F-theory geometries.Comment: 18 page

Multi-Instanton Calculus and Equivariant Cohomology

We present a systematic derivation of multi-instanton amplitudes in terms of ADHM equivariant cohomology. The results rely on a supersymmetric formulation of the localization formula for equivariant forms. We examine the cases of N=4 and N=2 gauge theories with adjoint and fundamental matter.Comment: 29 pages, one more reference adde

Fracture toughness of AlSi10Mg alloy produced by direct energy deposition with different crack plane orientations

The fracture and tensile behaviors of the AlSi10Mg alloy processed by Direct Energy Deposition were investigated. Three-point bending fracture toughness and tensile specimens were tested at room temperature along different crack plane orientations and loading directions. Before being machined and tested, the printed samples were subjected to heat treatment at 300 °C for 2 h to relieve the residual stresses. Microstructural and fractographic analyses were performed to investigate the fracture mechanisms and the crack propagation paths for each crack orientation. Significant differences in the fracture toughness were observed among the crack plane orientations. Specimens with cracks oriented in the X-Y direction featured the highest fracture toughness values (JIc = 11.96 kJ/m2), whereas the Z-Y crack orientation (perpendicular to the printing direction) performed the lowest fracture toughness values (JIc = 8.91 kJ/m2). The anisotropy in fracture toughness is mainly related to a preferential crack propagation path along the melt pool boundaries. At melt pool boundaries, pores are preferentially placed, coarsening of the microstructure occurs and there is higher Si content, leading to that area being less ductile and less resistant to crack propagation

Instantons on ALE spaces and Super Liouville Conformal Field Theories

We provide evidence that the conformal blocks of N=1 super Liouville conformal field theory are described in terms of the SU(2) Nekrasov partition function on the ALE space O_{P^1}(-2).Comment: 10 page

Quantitative lung ultrasonography: A putative new algorithm for automatic detection and quantification of B-lines

Background: This pilot study was designed to develop a fully automatic and quantitative scoring system of B-lines (QLUSS: quantitative lung ultrasound score) involving the pleural line and to compare it with previously described semi-quantitative scores in the measurement of extravascular lung water as determined by standard thermo-dilution. Methods: This was a prospective observational study of 12 patients admitted in the intensive care unit with acute respiratory distress and each provided with 12 lung ultrasound (LUS) frames. Data collected from each patient consisted in five different scores, four semi-quantitative (nLUSS, cLUSS, qLUSS, %LUSS) and quantitative scores (QLUSS). The association between LUS scores and extravascular lung water (EVLW) was determined by simple linear regression (SLR) and robust linear regression (RLR) methods. A correlation analysis between the LUS scores was performed by using the Spearman rank test. Inter-observer variability was tested by computing intraclass correlation coefficient (ICC) in two-way models for agreement, basing on scores obtained by different raters blinded to patients' conditions and clinical history. Results: In the SLR, QLUSS showed a stronger association with EVLW (R 2 = 0.57) than cLUSS (R 2 = 0.45) and nLUSS (R 2 = 0.000), while a lower association than qLUSS (R 2 = 0.85) and %LUSS (R 2 = 0.72) occurred. By applying RLR, QLUSS showed an association for EVLW (R 2 = 0.86) comparable to qLUSS (R 2 = 0.85) and stronger than %LUSS (R 2 = 0.72). QLUSS was significantly correlated with qLUSS (r = 0.772; p = 0.003) and %LUSS (r = 0.757; p = 0.005), but not with cLUSS (r = 0.561; p = 0.058) and nLUSS (r = 0.105; p = 0.744). Moreover, QLUSS showed the highest ICC (0.998; 95%CI from 0.996 to 0.999) among the LUS scores. Conclusions: This study demonstrates that computer-aided scoring of the pleural line percentage affected by B-lines has the potential to assess EVLW. QLUSS may have a significant impact, once validated with a larger dataset composed by multiple real-time frames. This approach has the potentials to be advantageous in terms of faster data analysis and applicability to large sets of data without increased costs. On the contrary, it is not useful in pleural effusion or consolidations

Parafermionic Liouville field theory and instantons on ALE spaces

In this paper we study the correspondence between the $\hat{\textrm{su}}(n)_{k}\oplus \hat{\textrm{su}}(n)_{p}/\hat{\textrm{su}}(n)_{k+p}$ coset conformal field theories and $\mathcal{N}=2$ SU(n) gauge theories on $\mathbb{R}^{4}/\mathbb{Z}_{p}$. Namely we check the correspondence between the SU(2) Nekrasov partition function on $\mathbb{R}^{4}/\mathbb{Z}_{4}$ and the conformal blocks of the $S_{3}$ parafermion algebra (in $S$ and $D$ modules). We find that they are equal up to the U(1)-factor as it was in all cases of AGT-like relations. Studying the structure of the instanton partition function on $\mathbb{R}^4/\mathbb{Z}_p$ we also find some evidence that this correspondence with arbitrary $p$ takes place up to the U(1)-factor.Comment: 21 pages, 6 figures, misprints corrected, references added, version to appear in JHE

Glueball operators and the microscopic approach to N=1 gauge theories

We explain how to generalize Nekrasov's microscopic approach to N=2 gauge theories to the N=1 case, focusing on the typical example of the U(N) theory with one adjoint chiral multiplet X and an arbitrary polynomial tree-level superpotential Tr W(X). We provide a detailed analysis of the generalized glueball operators and a non-perturbative discussion of the Dijkgraaf-Vafa matrix model and of the generalized Konishi anomaly equations. We compute in particular the non-trivial quantum corrections to the Virasoro operators and algebra that generate these equations. We have performed explicit calculations up to two instantons, that involve the next-to-leading order corrections in Nekrasov's Omega-background.Comment: 38 pages, 1 figure and 1 appendix included; v2: typos and the list of references corrected, version to appear in JHE