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Resurgence in the bi-Yang-Baxter model
Nuclear Physics B ( IF 2.8 ) Pub Date : 2021-01-12 , DOI: 10.1016/j.nuclphysb.2021.115308
Lucas Schepers , Daniel C. Thompson

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=4 SU(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.



中文翻译:

bi-Yang-Baxter模型中的复活

我们研究了可积的Bi-Yang-Baxter变形 小号ü2主手性模型(PCM)及其有限作用单元解。在绝热压实下小号1个,我们获得了具有椭圆Lamé势的量子力学。

我们对该量子力学中的基态能量进行微扰计算,以大阶数获得渐近级数。使用Borel-Padé技术,我们确定了微扰级数的Borel平面中分支切口的预期位置,并表明它们与uniton动作的值匹配。因此,我们可以用绝热压实后分离出的uniton解来匹配对能量的非微扰贡献。

WKB分析的一个分支是确定该变形PCM与一个PCM的二次微分。 ñ=2Seiberg-Witten理论。这可以作为一个ñF=4 小号ü2 理论或椭圆振动 小号ü2×小号ü2理论。规范理论的质量参数由PCM的变形参数给出。

更新日期:2021-02-05
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