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 S1, 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 N=2 Seiberg-Witten theory. This can be done either as an Nf=4SU(2) theory or as an elliptic quiver SU(2)×SU(2) theory. The mass parameters of the gauge theory are given by the deformation parameters of the PCM.
Highlights
The task of computing exactly the values of observables in an interacting theory is typically, and certainly in the absence of simplifications afforded by supersymmetry or integrability, a difficult problem
Because the configuration with the lowest action yields the biggest contribution in perturbation theory, we divide the parameter space spanned by η and ζ into different regions, based on inequalities among the actions (3.5) and (3.11)
To complete the identification we must match the hypermultiplet masses to the parameters of the Schrodinger the system and the result is quite striking; we find that they are directly given by the parameters that control the underlying quantum group symmetry of the YB deformed principal chiral model (PCM)
Summary
The task of computing exactly the values of observables in an interacting theory is typically, and certainly in the absence of simplifications afforded by supersymmetry or integrability, a difficult problem. Adiabaticity, achieved essentially by including a twist in the reduction, is used to argue that the lower dimensional theory still encapsulates the key feature of the higher dimensional one Following this approach, it is possible to identify two-dimensional non-perturbative field configurations (so called unitons rather than instantons in the cases we study) as the origin of the objects that give rise to factorial behaviour in the reduced QM. It is possible to identify two-dimensional non-perturbative field configurations (so called unitons rather than instantons in the cases we study) as the origin of the objects that give rise to factorial behaviour in the reduced QM This is a crucial first step in establishing the resurgent nature of the QFT. We close with a discussion of a number of possible future directions
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