On a singular Fredholm-type integral equation arising in N=2 super Yang-Mills theories

In this work we study the Nekrasov-Shatashvili limit of the Nekrasov instanton partition function of Yang-Mills field theories with N=2 supersymmetry and gauge group SU(n). The theories are coupled with fundamental matter. The equation that determines the density of eigenvalues at the leading order in the saddle-point approximation is exactly solved. The dominating contribution to the instanton free energy is computed. The requirement that this energy is finite imposes quantization conditions on the parameters of the theory that are in agreement with analogous conditions that have been derived in previous works. Using methods borrowed from the theory of matrix models, a field theoretical expression of the full instanton partition function is derived. It is checked that in the Nekrasov-Shatashvili (thermodynamic) limit the action of the field theory obtained in this way reproduces exactly the equation of motion used in the saddle-point calculations.Comment: 16 pages, LaTeX + RevTex 4, no figures, final version accepted by Phys. Lett.

Superspin chains and supersymmetric gauge theories

We discuss the possible extensions of Bethe/gauge correspondence to quantum integrable systems based on the super-Lie algebras of A type. Along the way we propose the analogues of Nakajima quiver varieties whose cohomology and K-theory should carry the representations of the corresponding Yangian and the quantum affine algebras, respectively. We end up with comments on the N=4 planar super-Yang-Mills theory in four dimensions.Comment: 19 page

Streaming cold cosmic ray back-reaction and thermal instabilities across the background magnetic field

Using the multi-fluid approach, we investigate streaming and thermal instabilities of the electron-ion plasma with homogeneous cold cosmic rays drifting perpendicular to the background magnetic field. Perturbations across the magnetic field are considered. The back-reaction of cosmic rays resulting in the streaming instability is taken into account. The thermal instability is shown not to be subject to the action of cosmic rays in the model under consideration. The dispersion relation for the thermal instability has been derived which includes sound velocities of plasma and cosmic rays, Alfv\'{e}n and cosmic ray drift velocities. The relation between these parameters determines the kind of thermal instability from Parker's to Field's type instability. The results obtained can be useful for a more detailed the investigation of electron-ion astrophysical objects such as galaxy clusters including the dynamics of streaming cosmic rays.Comment: Submitted to MNRAS. arXiv admin note: substantial text overlap with arXiv:1203.573