Non-perturbative corrections to line defect integrated correlators in Sp(N) SCFTs

Abstract / Extracted Text

Latest Summary

Actionable Steps

• Apply the Toda chain equation to express large-N coefficients for integrated correlators with Wilson line insertion in Sp(N) SCFTs.
• Use Bessel function-based resummation for exact analytic expressions capturing non-perturbative corrections, especially when perturbative expansions truncate.
• Employ numerical Borel-Padé and resurgent techniques for asymptotic series with infinite terms to analyze singularities in the Borel plane and extract non-perturbative data.
• Generalize the strong-coupling resummation method to other N=2 SCFT contexts and observables involving similar matrix model integrals.
• Utilize the introduced methodology for observables beyond those with a single Bessel J function, extending to cases with double Bessel function integrals.
• Compare and supplement resurgence-based predictions with Cheshire cat resurgence when standard techniques do not apply.
• Integrate a step of cross-verifying numerical predictions with analytic or semi-analytic expressions for consistency.
• Investigate the holographic dual interpretation of non-perturbative corrections in AdS5 × S^5/Γ string backgrounds, guided by Wilson line results.

Key Findings

• For N=4 SYM and N=2 Sp(N) SCFTs, integrated correlators with line defect insertions display non-trivial non-perturbative corrections at strong coupling.
• In the N=2 case, perturbative strong-coupling expansions often truncate, requiring specialized (e.g., Bessel-function or Cheshire cat) resurgence techniques.
• A novel analytic resummation method using Bessel Kν functions allows exact-in-coupling non-perturbative results for cases with truncated expansions.
• For the N=4 SYM case, non-perturbative corrections are determined numerically by investigating branch cuts and pole structures in the Borel plane of asymptotic series.
• Borel-Padé analysis reveals singularities at t=±2 in the Borel plane, signaling the leading exponential corrections of order e^{-2√λ}.
• Next-to-planar corrections can contain both infinite asymptotic and truncated components, requiring a tailored combination of numerical and analytic resurgent techniques.
• Analytic and numerical resurgence techniques are complementary and allow cross-verification of non-perturbative predictions.
• Closed formulae for non-perturbative corrections have been provided for both planar and subleading large-N terms.

Practical Takeaways

• Use the analytic Bessel resummation for strong-coupling expansions with truncated perturbative series in supersymmetric gauge theories.
• Apply numerical Borel-Padé and resurgence analysis to extract non-perturbative information from infinite asymptotic perturbative expansions.
• The mixed analytic-numerical methodology developed is extendable to other N=2 SCFTs and observables amenable to matrix model representation.
• Resurgence and Borel-plane analysis can effectively reveal the structure and magnitude of non-perturbative effects in observables inaccessible to traditional perturbation theory.
• The new method provides closed-form analytic results, facilitating expansions, comparisons, and further analytical work in strong coupling regimes.
• Anticipate applications of these non-perturbative computations in constraining bootstrap analyses and in matching field theory results with holographic dual predictions.
• Upcoming research can further generalize these methods to more complex observables involving higher correlations and multiple Bessel functions.

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