Resurgence in the Bi-Yang-Baxter Model

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 Lamé-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-Padé 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.

50 pages, 18 figures

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Cited by in corpus (6)

• Exact-WKB analysis for SUSY and quantum deformed potentials: Quantum mechanics with Grassmann fields and Wess-Zumino terms
• Existence and Uniqueness of Exact WKB Solutions for Second-Order Singularly Perturbed Linear ODEs
• Quantum phase transition and Resurgence: Lessons from 3d $\mathcal{N}=4$ SQED
• Asymptotics in an Asymptotic CFT
• Asymptotics in the bi-Yang-Baxter Sigma Model
• Nonperturbative features in the Lie-algebraic Kähler sigma model with fermions