Recursive-algebraic solution of the closed string tachyon vacuum equation
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866913145973374976 |
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| author | Kim, Manki |
| author_facet | Kim, Manki |
| contents | We develop a recursive algebraic framework for solving the closed string tachyon vacuum equation, derived from the hyperbolic recursion relations of Fırat and Valdes-Meller. We restrict to the sector of zero-momentum Lorentz-scalar states. Lorentz symmetry ensures that this sector is closed under the equations of motion. In this sector, we introduce a seam-graded expansion and show that the equation is entirely algebraic at every order: the unknown at each grade enters only through point evaluations at the systolic length, so each grade reduces to a matrix inversion with no Fredholm equations. The expansion is formal; convergence in the multi-level system is the subject of ongoing work. This work was conducted with a publicly available version of Claude Code (Anthropic, Claude Opus 4.6). The complete research repository, including all computations, adversarial review logs, and the full human-AI collaboration history, is publicly available at https://github.com/mk2427/csft-tachyon-vacuum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29926 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Recursive-algebraic solution of the closed string tachyon vacuum equation Kim, Manki High Energy Physics - Theory We develop a recursive algebraic framework for solving the closed string tachyon vacuum equation, derived from the hyperbolic recursion relations of Fırat and Valdes-Meller. We restrict to the sector of zero-momentum Lorentz-scalar states. Lorentz symmetry ensures that this sector is closed under the equations of motion. In this sector, we introduce a seam-graded expansion and show that the equation is entirely algebraic at every order: the unknown at each grade enters only through point evaluations at the systolic length, so each grade reduces to a matrix inversion with no Fredholm equations. The expansion is formal; convergence in the multi-level system is the subject of ongoing work. This work was conducted with a publicly available version of Claude Code (Anthropic, Claude Opus 4.6). The complete research repository, including all computations, adversarial review logs, and the full human-AI collaboration history, is publicly available at https://github.com/mk2427/csft-tachyon-vacuum. |
| title | Recursive-algebraic solution of the closed string tachyon vacuum equation |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2603.29926 |