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Resurgence in the Bi-Yang-Baxter Model

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arxiv 2007.03683 v1 pith:BYSVRHP3 submitted 2020-07-07 hep-th math-phmath.MP

Lucas Schepers , Daniel C. Thompson This is my paper · ORCID
classification hep-thmath-phmath.MP
keywords theoryunitonadiabaticbi-yang-baxtercompactificationdeformationellipticenergy
verification ladder T0 review T1 audit T2 compute T3 formal
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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.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. On the $1/c$ expansion in $2d$ CFTs with degenerate operators

    hep-th 2024-12 accept novelty 8.0 of 10

    The all-order 1/c expansion of Virasoro blocks for degenerate operators is Borel resummable except across Stokes lines, and the resurgent analysis reconstructs the full correlator and resolves forbidden singularities.

  2. The Yang-Baxter Sigma Model from Twistor Space

    hep-th 2026-02 unverdicted novelty 7.0 of 10

    Twistor-space 6d Chern-Simons theory with Yang-Baxter boundary conditions yields a 4d integrable field theory whose symmetry reduction is the 2d Yang-Baxter sigma model.

  3. Nonperturbative features in the Lie-algebraic K\"ahler sigma model with fermions

    hep-th 2024-12 conditional novelty 6.0 of 10

    In the deformed CP1 quantum mechanics with fermions, the nonperturbative ambiguity structure of the ground state energy persists, with the elongation parameter k conjectured to enter at three loops through g^4(k^2-1).

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