Resurgence of high-energy string amplitudes
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arXiv
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| Format: | Preprint |
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2026
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| author | Kervyn, Xavier Stieberger, Stephan |
| author_facet | Kervyn, Xavier Stieberger, Stephan |
| contents | We analyze the fixed-angle high-energy ($α' \to \infty$) structure of $n$-point tree-level string amplitudes from complementary perspectives: locally via saddle-point expansions, algebraically via difference equations and their asymptotic structure, analytically via Aomoto-Gauss-Manin connection and Mellin-Barnes representation, and geometrically via twisted intersection theory and Lefschetz thimbles. Using, in turn, saddle-point analysis and finite-difference equations in the kinematic variables, we show that the perturbative coefficients in the resulting asymptotic series in $1/α'$ are organized by Bernoulli-number data, rather than by the multiple zeta values characteristic of the low-energy $α' \to 0$ regime. Resurgence theory allows upgrading these divergent series to transseries whose Stokes data capture the analytic continuation between unphysical and physical kinematic regions in the form of non-perturbative monodromy contributions. We derive the transseries for four-point open string amplitudes explicitly. We also construct a differential and Mellin formulation which place their low- and high-energy expansions in a common analytic framework and unifies them as asymptotic sectors of the same underlying object. We extend the difference-equation analysis to $n \geq 5$, where it yields perturbative high-energy asymptotic expansions and leads naturally to a higher-rank connection problem. Finally, translating our asymptotic analysis into the language of twisted de Rham theory, we derive an alternative double-copy representation of the high-energy limit of closed-string amplitudes in terms of Lefschetz thimbles for any $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_07444 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Resurgence of high-energy string amplitudes Kervyn, Xavier Stieberger, Stephan High Energy Physics - Theory Mathematical Physics Algebraic Geometry Number Theory We analyze the fixed-angle high-energy ($α' \to \infty$) structure of $n$-point tree-level string amplitudes from complementary perspectives: locally via saddle-point expansions, algebraically via difference equations and their asymptotic structure, analytically via Aomoto-Gauss-Manin connection and Mellin-Barnes representation, and geometrically via twisted intersection theory and Lefschetz thimbles. Using, in turn, saddle-point analysis and finite-difference equations in the kinematic variables, we show that the perturbative coefficients in the resulting asymptotic series in $1/α'$ are organized by Bernoulli-number data, rather than by the multiple zeta values characteristic of the low-energy $α' \to 0$ regime. Resurgence theory allows upgrading these divergent series to transseries whose Stokes data capture the analytic continuation between unphysical and physical kinematic regions in the form of non-perturbative monodromy contributions. We derive the transseries for four-point open string amplitudes explicitly. We also construct a differential and Mellin formulation which place their low- and high-energy expansions in a common analytic framework and unifies them as asymptotic sectors of the same underlying object. We extend the difference-equation analysis to $n \geq 5$, where it yields perturbative high-energy asymptotic expansions and leads naturally to a higher-rank connection problem. Finally, translating our asymptotic analysis into the language of twisted de Rham theory, we derive an alternative double-copy representation of the high-energy limit of closed-string amplitudes in terms of Lefschetz thimbles for any $n$. |
| title | Resurgence of high-energy string amplitudes |
| topic | High Energy Physics - Theory Mathematical Physics Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2604.07444 |