RG-Whitham dynamics and complex Hamiltonian systems

RG-Whitham dynamics and complex Hamiltonian systems

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 syste...

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Main Authors: A. Gorsky, A. Milekhin
Format: Article
Language:English
Published: Elsevier 2015-06-01
Series:Nuclear Physics B
Online Access:http://www.sciencedirect.com/science/article/pii/S0550321315001108
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spelling doaj-0f8a857c66344565bff00c919e72ca402020-11-25T00:01:22ZengElsevierNuclear Physics B0550-32132015-06-018953363RG-Whitham dynamics and complex Hamiltonian systemsA. Gorsky0A. Milekhin1Institute for Information Transmission Problems, B. Karetnyi 15, Moscow 127051, Russia; Moscow Institute of Physics and Technology, Dolgoprudny 141700, RussiaInstitute for Information Transmission Problems, B. Karetnyi 15, Moscow 127051, Russia; Moscow Institute of Physics and Technology, Dolgoprudny 141700, Russia; Institute for Theoretical and Experimental Physics, B. Cheryomushkinskaya 25, Moscow 117218, Russia; Corresponding author.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.http://www.sciencedirect.com/science/article/pii/S0550321315001108
collection DOAJ
language English
format Article
sources DOAJ
author A. Gorsky
A. Milekhin
spellingShingle A. Gorsky
A. Milekhin
RG-Whitham dynamics and complex Hamiltonian systems
Nuclear Physics B
author_facet A. Gorsky
A. Milekhin
author_sort A. Gorsky
title RG-Whitham dynamics and complex Hamiltonian systems
title_short RG-Whitham dynamics and complex Hamiltonian systems
title_full RG-Whitham dynamics and complex Hamiltonian systems
title_fullStr RG-Whitham dynamics and complex Hamiltonian systems
title_full_unstemmed RG-Whitham dynamics and complex Hamiltonian systems
title_sort rg-whitham dynamics and complex hamiltonian systems
publisher Elsevier
series Nuclear Physics B
issn 0550-3213
publishDate 2015-06-01
description 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.
url http://www.sciencedirect.com/science/article/pii/S0550321315001108
work_keys_str_mv AT agorsky rgwhithamdynamicsandcomplexhamiltoniansystems
AT amilekhin rgwhithamdynamicsandcomplexhamiltoniansystems
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