2014/08/31 by A. Gorsky, A. Milekhin · 1 citation
Physics and Astronomy · #hep-th
paper · pdf · doi:10.1016/j.nuclphysb.2015.03.028
v3: 34 pages, several typos corrected, a reference added, to appear in Nuclear Physics B
arxiv created 2015/04/07 · arxiv updated 2015/04/08
Inspired by the Seiberg-Witten exact solution, we consider some aspects of the Hamiltonian dynamics with the complexified phase space focusing at the renormalization group(RG)-like Whitham behavior. We show that at the Argyres-Douglas(AD) point the number of degrees of freedom in Hamiltonian system effectively reduces and argue that anomalous dimensions at AD point coincide with the Berry indexes in classical mechanics. In the framework of Whitham dynamics AD point turns out to be a fixed point. We demonstrate that recently discovered Dunne-Ünsal relation in quantum mechanics relevant for the exact quantization condition exactly coincides with the Whitham equation of motion in the Omega - deformed theory.