Hitchin Equation, Singularity, and N=2 Superconformal Field Theories

We argue that Hitchin's equation determines not only the low energy effective theory but also describes the UV theory of four dimensional N=2 superconformal field theories when we compactify six dimensional $A_N$ $(0,2)$ theory on a punctured Riemann surface. We study the singular solution to Hitchin's equation and the Higgs field of solutions has a simple pole at the punctures; We show that the massless theory is associated with Higgs field whose residual is a nilpotent element; We identify the flavor symmetry associated with the puncture by studying the singularity of closure of the moduli space of solutions with the appropriate boundary conditions. For the mass-deformed theory the residual of the Higgs field is a semi-simple element, we identify the semi-simple element by arguing that the moduli space of solutions of mass-deformed theory must be a deformation of the closure of the moduli space of the massless theory. We also study the Seiberg-Witten curve by identifying it as the spectral curve of the Hitchin's system. The results are all in agreement with Gaiotto's results derived from studying the Seiberg-Witten curve of four dimensional quiver gauge theory.Comment: 42 pages, 20 figures, Hitchin's equation for N=2 theory is derived by comparing different order of compactification of six dimensional theory on T^2\times \Sigma. More discussion about flavor symmetries. Typos are correcte

Peculiarities of the phase transformation dynamics in bulk FeRh based alloys from magnetic and structural measurements

We analyze coexistence of antiferromagnetic and ferromagnetic phases in bulk iron-rhodium and its alloys with palladium, Fe50,4Rh49,6, Fe49,7Rh47,4Pd2,9 and Fe48,3Rh46,8Pd4,9, using neutron diffraction, magnetization and scanning Hall probe imaging. Temperature dependencies of the lattice parameters, AFM and FM phase weight fractions, and Fe magnetic moment values were obtained on cooling and heating across the AFM-FM transition. Substantial thermomagnetic hysteresis for the phases’ weight fractions and a relatively narrow one for the unit cell volume has been observed on cooling-heating. A clear dependence of hysteretic behavior on Pd concentration has been traced. Additional direct magnetic measurements of the spatial distribution of the phase transition are acquired using scanning Hall probe microscopy, which reveals the length scale of the phase coexistence and the spatial progression of the transition in the presence of external magnetic field. Also, the magnetic phase diagram has been constructed for a series of Pd-doped FeRh alloys