Resurgence in the Bi-Yang-Baxter Model

TL;DR

This paper explores the integrable bi-Yang-Baxter deformation of the SU(2) principal chiral model, analyzing its quantum mechanics, non-perturbative effects, and connections to Seiberg-Witten theory, revealing new insights into its solutions and structure.

Contribution

It introduces a detailed analysis of the bi-Yang-Baxter deformed PCM, including perturbative and non-perturbative energy calculations and links to supersymmetric gauge theories.

Findings

Matching of non-perturbative energy contributions with uniton actions.

Identification of the PCM's quadratic differential with Seiberg-Witten theory.

Asymptotic series for ground state energy and Borel plane analysis.

Abstract

We study the integrable bi-Yang-Baxter deformation of the $SU(2)$ principal chiral model (PCM) and its finite action uniton solutions. Under an adiabatic compactification on an $S^1$, we obtain a quantum mechanics with an elliptic Lam\'e-like potential. We perform a perturbative calculation of the ground state energy in this quantum mechanics to large orders obtaining an asymptotic series. Using the Borel-Pad\'e technique, we determine the expected locations of branch cuts in the Borel plane of the perturbative series and show that they match the values of the uniton actions. Therefore, we can match the non-perturbative contributions to the energy with the uniton solutions which fractionate upon adiabatic compactification. An off-shoot of the WKB analysis, is to identify the quadratic differential of this deformed PCM with that of an $\mathcal{N}=2$ Seiberg-Witten theory. This can be done either as an $N_f=4$ $SU(2)$ theory or as an elliptic quiver $SU(2)\times SU(2)$ theory. The mass parameters of the gauge theory are given by the deformation parameters of the PCM.