Open-Closed String Field Theory from Calabi-Yau Categories and its Applications to Enumerative Geometry
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917356210487296 |
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| author | Ulmer, Jakob |
| author_facet | Ulmer, Jakob |
| contents | The overarching goal of this thesis was to develop categorical methods that connect enumerative geometry, as studied in mirror symmetry, with large $N$ gauge theories. In the first part, we established a relation between graph complexes, Calabi-Yau $A_\infty$-categories, and Kontsevich's cocycle construction. The next main result is the construction of a formality $L_\infty$-morphism relating algebraic structures built from a Calabi-Yau category and one of its objects; this morphism depends on a splitting of the non-commutative Hodge filtration. This generalizes the approach of categorical enumerative invariants from the closed to the open-closed setting. From a physics perspective, closed categorical enumerative invariants are encoded by the partition function of the associated closed string field theory (SFT). We explain how our open-closed morphism is an ingredient in quantizing the large N open SFT associated to an object of a Calabi-Yau category. In the final part of this thesis, based on an algebraic approach to open and closed backreacted SFT, we propose ideas towards a categorical formulation of 'Twisted Holography' at the level of partition functions, given as input a Calabi-Yau category and one of its objects. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_18186 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Open-Closed String Field Theory from Calabi-Yau Categories and its Applications to Enumerative Geometry Ulmer, Jakob Quantum Algebra High Energy Physics - Theory Mathematical Physics Symplectic Geometry The overarching goal of this thesis was to develop categorical methods that connect enumerative geometry, as studied in mirror symmetry, with large $N$ gauge theories. In the first part, we established a relation between graph complexes, Calabi-Yau $A_\infty$-categories, and Kontsevich's cocycle construction. The next main result is the construction of a formality $L_\infty$-morphism relating algebraic structures built from a Calabi-Yau category and one of its objects; this morphism depends on a splitting of the non-commutative Hodge filtration. This generalizes the approach of categorical enumerative invariants from the closed to the open-closed setting. From a physics perspective, closed categorical enumerative invariants are encoded by the partition function of the associated closed string field theory (SFT). We explain how our open-closed morphism is an ingredient in quantizing the large N open SFT associated to an object of a Calabi-Yau category. In the final part of this thesis, based on an algebraic approach to open and closed backreacted SFT, we propose ideas towards a categorical formulation of 'Twisted Holography' at the level of partition functions, given as input a Calabi-Yau category and one of its objects. |
| title | Open-Closed String Field Theory from Calabi-Yau Categories and its Applications to Enumerative Geometry |
| topic | Quantum Algebra High Energy Physics - Theory Mathematical Physics Symplectic Geometry |
| url | https://arxiv.org/abs/2603.18186 |