RG-Whitham dynamics and complex Hamiltonian systems

Understand

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-\"Unsal relation in quantum mechanics relevant for the exact quantization condition exactly coincides with the Whitham equation of motion in the Omega - deformed theory.