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We present an explicit non-perturbative solution of N =2 supersymmetric SU (N ) gauge theory with N f ≤ 2N flavors generalizing results of Seiberg and Witten for N = 2.

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The problem of swimming a t low Reynolds number is formulated in terms of a gauge field on the space of shapes. Effective methods for computing this field, by solving a linear boundary-value problem, are described. We employ conformal-mapping techniques to calculate swimming motions for cylinders with a variety of crosssections. We also determine the net translational motion due to arbitrary infinitesimal deformations of a sphere.

We present a general method for computing the central charges a and c of N = 2 superconformal field theories corresponding to singular points in the moduli space of N = 2 gauge theories. Our method relates a and c to the U(1) R anomalies of the topologically twisted gauge theory. We evaluate these anomalies by studying the holomorphic dependence of the path integral measure on the moduli. We calculate a and c for superconformal points in a variety of gauge theories, including N = 4 SU(N), N = 2 pure SU(N) Yang-Mills, and USp(2N) with 1 massless antisymmetric and 4 massive fundamental hypermultiplets. In the latter case, we reproduce the conformal and flavor central charges previously calculated using the gravity duals of these gauge theories. For any SCFT in the class under consideration, we derive a previously conjectured expression for 2a − c in terms of the sum of the dimensions of operators parameterizing the Coulomb branch. Finally, we prove that the ratio a/c is bounded above by 5/4 and below by 1/2.