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

Lorenzo De Lillo, Alessandro Pini

TL;DR

This work addresses non-perturbative corrections to line-defect integrated correlators in Sp(N) SCFTs, analyzing both N=4 SYM and a specific N=2 theory using localization and a Toda-chain framework. It introduces a novel strong-coupling resummation method, yielding exact analytic results for the N=2 case and enabling explicit non-perturbative expansions for the N=4 case, including leading exponential corrections of the form $e^{-\sqrt{\lambda}}$ and $e^{-2\sqrt{\lambda}}$. The results connect to holography via AdS$_5$×S$^5$/ℤ$_2$, where worldsheet instantons offer a gravity-side interpretation of the non-perturbative effects. Overall, the paper provides a robust, broadly applicable approach that unifies localization, Toda-chain structure, and resurgence to extract physically meaningful non-perturbative information for line-defect observables across different supersymmetric theories.

Abstract

We consider the $\mathcal{N}=4$ SYM theory with gauge group $Sp(N)$ and the $\mathcal{N}=2$ superconformal field theory consisting of four hypermultiplets in the fundamental representation and one hypermultiplet in the rank-two antisymmetric representation of the $Sp(N)$ gauge group. Building on previous results obtained via supersymmetric localization and a Toda equation, we determine the leading non-perturbative corrections at strong coupling to the integrated correlator between a Wilson line and two Higgs-branch moment map operators. In the case of the $\mathcal{N}=2$ SCFT, the presence of truncated asymptotic expansions led us to develop a resurgent method complementary to Cheshire cat resurgence. This approach has the advantage of yielding an exact expression for the correlator in terms of an analytic function, which can subsequently be expanded in the strong-coupling regime.

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

TL;DR

This work addresses non-perturbative corrections to line-defect integrated correlators in Sp(N) SCFTs, analyzing both N=4 SYM and a specific N=2 theory using localization and a Toda-chain framework. It introduces a novel strong-coupling resummation method, yielding exact analytic results for the N=2 case and enabling explicit non-perturbative expansions for the N=4 case, including leading exponential corrections of the form and . The results connect to holography via AdS×S/ℤ, where worldsheet instantons offer a gravity-side interpretation of the non-perturbative effects. Overall, the paper provides a robust, broadly applicable approach that unifies localization, Toda-chain structure, and resurgence to extract physically meaningful non-perturbative information for line-defect observables across different supersymmetric theories.

Abstract

We consider the SYM theory with gauge group and the superconformal field theory consisting of four hypermultiplets in the fundamental representation and one hypermultiplet in the rank-two antisymmetric representation of the gauge group. Building on previous results obtained via supersymmetric localization and a Toda equation, we determine the leading non-perturbative corrections at strong coupling to the integrated correlator between a Wilson line and two Higgs-branch moment map operators. In the case of the SCFT, the presence of truncated asymptotic expansions led us to develop a resurgent method complementary to Cheshire cat resurgence. This approach has the advantage of yielding an exact expression for the correlator in terms of an analytic function, which can subsequently be expanded in the strong-coupling regime.
Paper Structure (15 sections, 144 equations, 3 figures)

This paper contains 15 sections, 144 equations, 3 figures.

Table of Contents

  1. Introduction
  2. The $Sp(N)$ theories and the corresponding matrix models
  3. Toda chain and $Sp(N)$ SCFTs
  4. Toda chain at large $N$
  5. Non-perturbative corrections in the $\mathcal{N}=2$ $Sp(N)$ theory
  6. An alternative route to non-perturbative corrections for truncated series
  7. The non-perturbative strong coupling expansions of $\mathcal{I}$
  8. Non-perturbative corrections in the $\mathcal{N}=4$ SYM theory
  9. The planar term
  10. The next to planar term
  11. Conclusions
  12. Comparison with Cheshire cat resurgence
  13. Closed-form expression for $\widehat{\mathcal{K}}^{(0)}$
  14. The integral \ref{['K0integral']} and Dominated Convergence Theorem
  15. Single- and double-pole contributions

Figures (3)

  • Figure 1: Poles of the diagonal Borel-Padé approximant $PB_{[100/100]}[\widetilde{\mathcal{I}}^{(0)}/\sqrt{\lambda}]$. The poles are in $t$-variable after the transformation \ref{['BorelI0']}.
  • Figure 2: The sequence $A_n^{\text{even}}$ defined in \ref{['eq:AEvenModule']} is shown on the left, while the sequence $A_n^{\text{odd}}$\ref{['eq:AOddModule']} constructed from the odd coefficients is shown on the right. In both cases, the numerical data seem to converge very rapidly to the value $2$.
  • Figure 3: The integration contour in the Borel plane is indicated by the blue line, the black dot represents the singularity at $t=A$, and the red line denotes the branch cut along the positive real axis.