Demulder, S. and Dorigoni, D. and Thompson, D. (2016) 'Resurgence in η-deformed Principal Chiral Models.', Journal of high energy physics., 2016 (07). 088.
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.
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|Publisher Web site:||https://doi.org/10.1007/JHEP07(2016)088|
|Publisher statement:||Open Access, © The Author(s). 2016 Article funded by SCOAP3. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.|
|Date accepted:||30 June 2016|
|Date deposited:||06 March 2017|
|Date of first online publication:||18 July 2016|
|Date first made open access:||06 March 2017|
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