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Resurgence in η-deformed Principal Chiral Models

Saskia Demulder, Daniele Dorigoni, Daniel Thompson Orcid Logo

Journal of High Energy Physics, Volume: 2016, Issue: 7

Swansea University Author: Daniel Thompson Orcid Logo

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DOI (Published version): 10.1007/jhep07(2016)088

Abstract

We study the SU(2) Principal Chiral Model (PCM) in the presence of an integrable η-deformation. We put the theory on R×S1 with twisted boundary conditions and then reduce the circle to obtain an effective quantum mechanics associated with the Whittaker-Hill equation. Using resurgent analysis we stud...

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Published in: Journal of High Energy Physics
ISSN: 1029-8479
Published: Springer Science and Business Media LLC 2016
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa33814
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Abstract: We study the SU(2) Principal Chiral Model (PCM) in the presence of an integrable η-deformation. We put the theory on R×S1 with twisted boundary conditions and then reduce the circle to obtain an effective quantum mechanics associated with the Whittaker-Hill equation. Using resurgent analysis we study the large order behaviour of perturbation theory and recover the fracton events responsible for IR renormalons. The fractons are modified from the standard PCM due to the presence of this η-deformation but they are still the constituents of uniton-like solutions in the deformed quantum field theory. We also find novel SL(2,ℂ) saddles, thus strengthening the conjecture that the semi-classical expansion of the path integral gives rise to a resurgent transseries once written as a sum over Lefschetz thimbles living in a complexification of the field space. We conclude by connecting our quantum mechanics to a massive deformation of the N=2 4-d gauge theory with gauge group SU(2) and Nf=2.
Keywords: Nonperturbative Effects; Sigma Models; Integrable Field Theories; Solitons Monopoles and Instantons
College: Faculty of Science and Engineering
Issue: 7

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