Resurgence in η-deformed Principal Chiral Models

Demulder, S.; Dorigoni, D.; Thompson, D.

Abstract

We study the SU(2) Principal Chiral Model (PCM) in the presence of an integrable η-deformation. We put the theory on R×S1R×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)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 NN = 2 4-d gauge theory with gauge group SU(2) and Nf = 2.

Citation

Demulder, S., Dorigoni, D., & Thompson, D. (2016). Resurgence in η-deformed Principal Chiral Models. Journal of High Energy Physics, 2016(07), Article 088. https://doi.org/10.1007/jhep07%282016%29088

• Journal Article Type: Article
• Acceptance Date: Jun 30, 2016
• Online Publication Date: Jul 18, 2016
• Publication Date: Jul 18, 2016
• Deposit Date: Mar 3, 2017
• Publicly Available Date: Mar 6, 2017
• Journal: Journal of High Energy Physics
• Print ISSN: 1126-6708
• Electronic ISSN: 1029-8479
• Publisher: Scuola Internazionale Superiore di Studi Avanzati (SISSA)
• Peer Reviewed: Peer Reviewed
• Volume: 2016
• Issue: 07
• Article Number: 088
• DOI: https://doi.org/10.1007/jhep07%282016%29088
• Public URL: https://durham-repository.worktribe.com/output/1384054