RG-Whitham dynamics and complex Hamiltonian systems

A. Gorsky; A. Milekhin

doi:10.1016/j.nuclphysb.2015.03.028

RG-Whitham dynamics and complex Hamiltonian systems

A. Gorsky
, A. Milekhin

Physics And Astronomy

Research output: Contribution to journal › Article › peer-review

25 Scopus citations

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 Ω-deformed theory.

Original language	English
Pages (from-to)	33-63
Number of pages	31
Journal	Nuclear Physics B
Volume	895
DOIs	https://doi.org/10.1016/j.nuclphysb.2015.03.028
State	Published - Jun 1 2015

Bibliographical note

Publisher Copyright:
© 2015 The Authors.

Funding

The research was carried out at the IITP RAS at the expense of the Russian Foundation for Sciences (project No. 14-50-00150 ). We would like to thank G. Basar, K. Bulycheva, A. Kamenev, G. Korchemsky, P. Koroteev, A. Marshakov, A. Mironov, A. Morozov, A. Neitzke and B. Runov for the useful discussions and comments. We are especially grateful to I. Krichever for the careful reading of our manuscript.

Funders	Funder number
Russian Science Foundation	14-50-00150

ASJC Scopus subject areas

Nuclear and High Energy Physics

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10.1016/j.nuclphysb.2015.03.028

Cite this

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RG-Whitham dynamics and complex Hamiltonian systems

Abstract

Bibliographical note

Funding

ASJC Scopus subject areas

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