Exact Solutions to Matrix Models and String Theories: The Local Construction
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arXiv
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| Format: | Preprint |
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2026
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| author | Kager, Jasper Rodrigues, João Schiappa, Ricardo Schwick, Maximilian Tamarin, Noam |
| author_facet | Kager, Jasper Rodrigues, João Schiappa, Ricardo Schwick, Maximilian Tamarin, Noam |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_15101 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Exact Solutions to Matrix Models and String Theories: The Local Construction Kager, Jasper Rodrigues, João Schiappa, Ricardo Schwick, Maximilian Tamarin, Noam High Energy Physics - Theory Statistical Mechanics Mathematical Physics Exactly Solvable and Integrable Systems 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. |
| title | Exact Solutions to Matrix Models and String Theories: The Local Construction |
| topic | High Energy Physics - Theory Statistical Mechanics Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2602.15101 |