http://inspirehep.net/record/499969/files/arXiv:hep-th_9905111.pdf

Large N Field Theories, String Theory and Gravity

Type iib superstrings, bps monopoles, and three-dimensional gauge dynamics

We consider BPS states in a large class of d=4, N=2 field theories, obtained by reducing six-dimensional (2,0) superconformal field theories on Riemann surfaces, with defect operators inserted at points of the Riemann surface. Further dimensional reduction on S^1 yields sigma models, whose target spaces are moduli spaces of Higgs bundles on Riemann surfaces with ramification. In the case where the Higgs bundles have rank 2, we construct canonical Darboux coordinate systems on their moduli spaces. These coordinate systems are related to one another by Poisson transformations associated to BPS states, and have well-controlled asymptotic behavior, obtained from the WKB approximation. The existence of these coordinates implies the Kontsevich-Soibelman wall-crossing formula for the BPS spectrum. This construction provides a concrete realization of a general physical explanation of the wall-crossing formula which was proposed in 0807.4723. It also yields a new method for computing the spectrum using the combinatorics of triangulations of the Riemann surface.

Wall-crossing, Hitchin Systems, and the WKB Approximation

Mirror symmetry in three dimensional gauge theories

The exact superconformal R-symmetry maximizes a

New N = 2 superconformal field theories in four dimensions

The moduli space of vacua of N = 2 SUSY QCD and duality in N = 1 SUSY QCD

New examples of N=2 supersymmetric conformal field theories are found as fixed points of SU(2) N=2 supersymmetric QCD. Relations among the scaling dimensions of their relevant chiral operators, global symmetries, and Higgs branches are understood in terms of the general structure of relevant deformations of non-trivial N=2 conformal field theories. The spectrum of scaling dimensions found are all those compatible with relevant deformations of a y^2 = x^3 singular curve.

New N=2 Superconformal Field Theories in Four Dimensions

We analyze in detail the moduli space of vacua of N=2 SUSY QCD with n_c colors and n_f flavors. The Coulomb branch has submanifolds with non-Abelian gauge symmetry. The massless quarks and gluons at these vacua are smoothly connected to the underlying elementary quarks and gluons. Upon breaking N=2 by an N=1 preserving mass term for the adjoint field the theory flows to N=1 SUSY QCD. Some of the massless quarks and gluons on the moduli space of the N=2 theory become the magnetic quarks and gluons of the N=1 theory. In this way we derive the duality in N=1 SUSY QCD by identifying its crucial building blocks---the magnetic degrees of freedom---using only semiclassical physics and the non-renormalization theorem.

Philip C. Argyres

Papers

New N = 2 superconformal field theories in four dimensions

The moduli space of vacua of N = 2 SUSY QCD and duality in N = 1 SUSY QCD

New N=2 Superconformal Field Theories in Four Dimensions

The Moduli Space of N=2 SUSY QCD and Duality in N=1 SUSY QCD

The vacuum structure of N = 2 super-QCD with classical gauge groups