Noam Tamarin | Searcharxiv

arXiv2026

All the D-Branes of Resurgence

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.

hep-th↗

arXiv2026

Exact Solutions to Matrix Models and String Theories: The Local Construction

Exact nonperturbative solutions to hermitian one-matrix models, their topological string duals, as well as their double-scaling limits to multicritical and minimal string theories, may be obtained via the use of resurgent transseries. These solutions are generically resonant, entailing both eigenvalues and anti-eigenvalues, or, equivalently, both D-branes and negative-tension D-branes -- but are otherwise intricate to write down, having been previously addressed on a case-by-case approach. This work shows how there is a general and rather compact way to write down all these exact and fully nonperturbative transseries solutions in closed-form, immediately starting from the spectral geometry of the matrix model or string theory at hand, in the form of a discrete Fourier or Zak transform for their partition functions. This structure is inherently associated to the existence of anti-eigenvalues or negative-tension D-branes. The validity of these solutions is testable across all values of the parameters -- from weak to strong 't Hooft coupling, from small to large N; equivalently, from semi-classical to deeply quantum regimes -- and many such nonperturbative tests are performed against diverse examples ranging from matrix models to non-critical strings, fully validating our analytical and exact expressions. In particular, anti-eigenvalues or negative-tension D-branes are absolutely required to find sharp numerical matches. In order to study these solutions globally across their phase diagrams, however, complete non-linear Stokes data is still needed -- which will be addressed in a complementary follow-up paper.

hep-th↗