All the D-Branes of Resurgence

TL;DR

This paper explores the role of negative-tension D-branes in resurgence theory, extending matrix model and Liouville field theory analyses to minimal strings, JT gravity, and topological strings, revealing new nonperturbative sectors.

Contribution

It introduces negative-tension ZZ-branes as essential for resurgence and develops a unified framework for nonperturbative sectors across string theories using matrix models and conformal field theory.

Findings

Negative-tension ZZ-branes correspond to anti-eigenvalues in matrix models.

Constructed minimal-string free-energy transseries with resurgent Stokes data.

Extended analysis to JT gravity, topological strings, and AdS spacetime with consistent checks.

Abstract

It was recently shown how to account for all instantons of hermitian matrix models via (anti-) eigenvalue-tunneling -- including both exponentially-suppressed and exponentially-enhanced transseries-transmonomials which are predicted by resurgence. Matrix-model eigenvalue-tunneling corresponds to ZZ-branes. The present work shows how matrix-model anti-eigenvalues correspond to negative-tension ZZ-branes; and how to compute generic nonperturbative sectors -- with both ZZ and negative-tension-ZZ branes -- in the minimal-string free-energy. Negative-tension D-branes are herein a requirement of resurgence. This results in the construction of minimal-string free-energy transseries and the analytic computation of their resurgent Stokes data. Calculations are presented via Liouville boundary conformal field theory and via (matching) matrix model analysis. Minimal-string results are extended to Jackiw-Teitelboim gravity. Building on the matrix model analysis, one extension towards topological string theory is obtained via the remodeling-conjecture -- which allows for addressing one-cut, toric Calabi-Yau geometries. Building on the Liouville theory calculation, one other extension towards critical string theory is obtained via the H3+ - Liouville correspondence -- which allows for addressing negative-tension D-instantons in AdS spacetime. Throughout, checks of the construction and formulae are made in several examples, against both Borel resurgent analysis and string-equation transseries data.