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Strong coupling structure of $\mathcal{N}=4$ SYM observables with matrix Bessel kernel

Bercel Boldis

Abstract

In this paper I continue the program of studying the strong coupling expansion of certain observables in $\mathcal{N}=4$ supersymmetric Yang--Mills theory, which are given by a determinant with a matrix Bessel kernel. I show that, by reorganizing the transseries of the determinant at large values of the 't Hooft coupling, a simple underlying structure emerges, in which each exponentially suppressed correction is related to the perturbative series in a simple way. This new approach provides an efficient method to generate the full transseries for $\mathcal{N}=4$ SYM observables, such as the cusp anomalous dimension, multi-gluon scattering amplitudes, and the octagon form factor. Using high-precision numerical analysis, I verify the results and provide a complete description of the resurgence structure of the strong coupling expansion.

Strong coupling structure of $\mathcal{N}=4$ SYM observables with matrix Bessel kernel

Abstract

In this paper I continue the program of studying the strong coupling expansion of certain observables in supersymmetric Yang--Mills theory, which are given by a determinant with a matrix Bessel kernel. I show that, by reorganizing the transseries of the determinant at large values of the 't Hooft coupling, a simple underlying structure emerges, in which each exponentially suppressed correction is related to the perturbative series in a simple way. This new approach provides an efficient method to generate the full transseries for SYM observables, such as the cusp anomalous dimension, multi-gluon scattering amplitudes, and the octagon form factor. Using high-precision numerical analysis, I verify the results and provide a complete description of the resurgence structure of the strong coupling expansion.
Paper Structure (11 sections, 149 equations, 2 figures)

This paper contains 11 sections, 149 equations, 2 figures.

Table of Contents

  1. Introduction and summary
  2. Strong coupling expansion
  3. The transseries structure from a different angle
  4. $1/g$ expansion
  5. Stokes constants
  6. A practical example
  7. Resurgence relations
  8. Stokes automorphism
  9. Asymptotic analysis
  10. Median resummation
  11. Bridge equations

Figures (2)

  • Figure 1: The horizontal axis denotes the powers of $\Lambda_-^{2}$, while the vertical one represents the powers of $\Lambda_+^{2}$. The colored squares correspond to corrections that satisfy \ref{['nonzero']}, hence give non-zero contribution to the strong coupling expansion. Different colors represent how many different contributions they contain from the $(\delta^+,\delta^-)$ representation.
  • Figure 2: The figures from top to bottom illustrate the cut structures of $\mathcal{B}\left[\mathcal{D}^{(\delta^+,\delta^-)}\right](s)$ on the Borel plane with $(\delta^+,\delta^-)=(\{\},\{\}),(\{0\},\{\})$ and $(\{0\},\{0\})$. The black lines represent cuts starting from the branch points on the real line and ending at infinity. The green lines represent which cuts has to be removed from the positive line to go from one correction to the next one. The red lines appearing on the negative real line denote the additional cuts compared to the previous correction.