RG-Whitham dynamics and complex Hamiltonian systems

Abstract

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.

v3: 34 pages, several typos corrected, a reference added, to appear in Nuclear Physics B

References in corpus (4)

• Seiberg-Witten Theory and Random Partitions
• Deforming SW curve
• Topological expansion of beta-ensemble model and quantum algebraic geometry in the sectorwise approach
• Exceptional points in quantum and classical dynamics

Cited by in corpus (4)

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• Pure N=2 Super Yang-Mills and Exact WKB
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