Towards Lefschetz Thimbles in Sigma Models, I

We study two dimensional path integral Lefschetz thimbles, i.e. the possible path integration contours. Specifically, in the examples of the O ( N ) and models, we find a large class of complex critical points of the sigma model actions which are relevant for the theory in finite volume at finite te...

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Bibliographic Details
Published in:Journal of experimental and theoretical physics 2021-04, Vol.132 (4), p.734-751
Main Authors: Krichever, I., Nekrasov, N.
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Critical point
Elementary Particles
Instantons
Particle and Nuclear Physics
Physics
Physics and Astronomy
Quantum Field Theory
Relativity Theory
Solid State Physics
Two dimensional models
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Summary:We study two dimensional path integral Lefschetz thimbles, i.e. the possible path integration contours. Specifically, in the examples of the O ( N ) and models, we find a large class of complex critical points of the sigma model actions which are relevant for the theory in finite volume at finite temperature, with various chemical potentials corresponding to the symmetries of the models. In this paper we discuss the case of the O (2 m ) and the models in the sector of zero instanton charge, as well as some solutions of the O (2 m + 1) model. The -model for all instanton charges and a more general class of solutions of the O ( N )-model with odd N will be discussed in the forthcoming paper.
ISSN:1063-7761
1090-6509
DOI:10.1134/S1063776121040129