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ODE/IM correspondence and quantum periods

Record Type:	Electronic resources : Monograph/item
Title/Author:	ODE/IM correspondence and quantum periods/ by Katsushi Ito, Hongfei Shu.
Author:	Ito, Katsushi.
other author:	Shu, Hongfei.
Published:	Singapore :Springer Nature Singapore : : 2025.,
Description:	x, 128 p. :ill. (some col.), digital ;24 cm.
[NT 15003449]:	ODE/IM Correspondence -- Exact WKB Analysis and TBA Equations -- Massive ODE/IM Correspondence -- Integrable Models and Functional Relations.
Contained By:	Springer Nature eBook
Subject:	Quantum field theory. -
Online resource:	https://doi.org/10.1007/978-981-96-0499-9
ISBN:	9789819604999

ODE/IM correspondence and quantum periods
Ito, Katsushi.

ODE/IM correspondence and quantum periods[electronic resource] /by Katsushi Ito, Hongfei Shu. - Singapore :Springer Nature Singapore :2025. - x, 128 p. :ill. (some col.), digital ;24 cm. - SpringerBriefs in mathematical physics,v. 512197-1765 ;. - SpringerBriefs in mathematical physics ;v. 51..

ODE/IM Correspondence -- Exact WKB Analysis and TBA Equations -- Massive ODE/IM Correspondence -- Integrable Models and Functional Relations.

This book is intended to review some recent developments in quantum field theories and integrable models. The ODE/IM correspondence, which is a nontrivial relation between the spectral analysis of ordinary differential equations and the functional relation approach to two-dimensional quantum integrable models, is the main subject. This correspondence was first discovered by Dorey and Tateo (and Bazhanov, Lukyanov, and Zamolodchikov) in 1998, where the relation between the Schrodinger equation with a monomial potential and the functional equation called the Y-system was found. This correspondence is an example of the mysterious link between classical and quantum integrable systems, which produces many interesting applications in mathematical physics, including exact WKB analysis, the quantum Seiberg-Witten curve, and the AdS-CFT correspondence. In this book, the authors explain some basic notions of the ODE/IM correspondence, where the ODE can be formulated as a linear problem associated with affine Toda field equations. The authors then apply the approach of the ODE/IM correspondence to the exact WKB periods in quantum mechanics with a polynomial potential. Deformation of the potential leads to wall-crossing phenomena in the TBA equations. The exact WKB periods can also be regarded as the quantum periods of the four-dimensional N=2 supersymmetric gauge theories in the Nekrasov-Shatashvili limit of the Omega background. The authors also explain the massive version of the ODE/IM correspondence based on the affine Toda field equations, which also has an application to the minimal surface, and the gluon scattering amplitudes in the AdS/CFT correspondence.

ISBN: 9789819604999

Standard No.: 10.1007/978-981-96-0499-9doiSubjects--Topical Terms:

523766
Quantum field theory.

LC Class. No.: QC174.45

Dewey Class. No.: 530.143

ODE/IM correspondence and quantum periods
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520 $a This book is intended to review some recent developments in quantum field theories and integrable models. The ODE/IM correspondence, which is a nontrivial relation between the spectral analysis of ordinary differential equations and the functional relation approach to two-dimensional quantum integrable models, is the main subject. This correspondence was first discovered by Dorey and Tateo (and Bazhanov, Lukyanov, and Zamolodchikov) in 1998, where the relation between the Schrodinger equation with a monomial potential and the functional equation called the Y-system was found. This correspondence is an example of the mysterious link between classical and quantum integrable systems, which produces many interesting applications in mathematical physics, including exact WKB analysis, the quantum Seiberg-Witten curve, and the AdS-CFT correspondence. In this book, the authors explain some basic notions of the ODE/IM correspondence, where the ODE can be formulated as a linear problem associated with affine Toda field equations. The authors then apply the approach of the ODE/IM correspondence to the exact WKB periods in quantum mechanics with a polynomial potential. Deformation of the potential leads to wall-crossing phenomena in the TBA equations. The exact WKB periods can also be regarded as the quantum periods of the four-dimensional N=2 supersymmetric gauge theories in the Nekrasov-Shatashvili limit of the Omega background. The authors also explain the massive version of the ODE/IM correspondence based on the affine Toda field equations, which also has an application to the minimal surface, and the gluon scattering amplitudes in the AdS/CFT correspondence.
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