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Splitting of surface defect partition functions and integrable systems

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arxiv 1709.04926 v2 pith:T7RRRUEG submitted 2017-09-14 hep-th math-phmath.MPnlin.SI

Saebyeok Jeong This is my paper
classification hep-thmath-phmath.MPnlin.SI
keywords defectgaugesurfacepartitionbethecoulombdegenerateequations
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We study Bethe/gauge correspondence at the special locus of Coulomb moduli where the integrable system exhibits the splitting of degenerate levels. For this investigation, we consider the four-dimensional pure $\mathcal{N}=2$ supersymmetric $U(N)$ gauge theory, with a half-BPS surface defect constructed with the help of an orbifold or a degenerate gauge vertex. We show that the non-perturbative Dyson-Schwinger equations imply the Schr\"odinger-type and the Baxter-type differential equations satisfied by the respective surface defect partition functions. At the special locus of Coulomb moduli the surface defect partition function splits into parts. We recover the Bethe/gauge dictionary for each summand.

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Cited by 4 Pith papers

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

  1. $Q$-operators, $q$-opers, and R-matrices in 5d $\mathcal{N}=1$ gauge theory

    hep-th 2025-07 conditional novelty 7.0 of 10

    In 5d N=1 U(N) gauge theory, codimension-two defects produce Q-operators whose q-difference equations are the Baxter TQ equations of XXZ spin chains built on bi-infinite evaluation modules of quantum affine algebras.

  2. Exact WKB of solutions by Borel summation and open TBA

    hep-th 2025-07 conditional novelty 7.0 of 10

    Borel-summed WKB solutions of quantum Seiberg-Witten equations are matched, numerically, to GMN open TBA solutions for the Weber and modified Mathieu equations.

  3. Blowing-up the edge: connection formulae and stability chart of the Lam\'e equation

    hep-th 2025-07 conditional novelty 7.0 of 10

    The paper derives the resummed Nekrasov-Shatashvili free energy from blow-up equations and uses it to compute the band-gap structure, connection formulas, and stability chart of the Lamé equation.

  4. Split Heun functions via blown-up surface defects

    hep-th 2026-07 accept novelty 6.5 of 10

    Blow-up equations for NS functions alone resum resonant poles of bulk and defect prepotentials, producing split Heun band-edge solutions, logarithmic companions, and nested mass loci for gap closure versus semisimple ...

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