Approaching Argyres-Douglas theories

The Seiberg-Witten solution to four-dimensional N = 2 super-Yang-Mills theory with gauge group SU(N) and without hypermultiplets is used to investigate the neighborhood of the maximal Argyres-Douglas points of type (a(1),a(N-1)). A convergent series expansion for the Seiberg-Witten periods near the Argyres-Douglas points is obtained by analytic continuation of the series expansion around the z(2N) symmetric point derived in arXiv:2208.11502. Along with direct integration of the Picard-Fuchs equations for the periods, the expansion is used to determine the location of the walls of marginal stability for SU(3). The intrinsic periods and Kahler potential of the (a(1),a(N-1)) superconformal fixed point are computed by letting the strong coupling scale tend to infinity. We conjecture that the resulting intrinsic Kahler potential is positive definite and convex, with a unique minimum at the Argyres-Douglas point, provided only intrinsic Coulomb branch operators with unitary scaling dimensions Delta > 1 acquire a vacuum expectation value, and provide both analytical and numerical evidence in support of this conjecture. In all the low rank examples considered here, it is found that turning on moduli dual to Delta <= 1 operators spoils the positivity and convexity of the intrinsic Kahler potential.