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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2408.00861 |
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| _version_ | 1866910551933714432 |
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| author | Kidambi, Abhiram Okada, Masaki Watari, Taizan |
| author_facet | Kidambi, Abhiram Okada, Masaki Watari, Taizan |
| contents | These notes combine results from two papers by the present authors viz., Part I (arXiv:2205.10299) and Part II (arXiv:2212.13028) into one streamlined version for better readability, along with a review on theory of complex multiplication for non-singular complex projective varieties and complex tori that is aimed at string theorists. We think that it is worth posting this edition as a separate entry in arXiv for those reasons, although this edition contains no essential progress beyond Part I and Part II.
S. Gukov and C. Vafa proposed a characterization of rational N=(1,1) superconformal field theories (SCFTs) on 1+1 dimensions with Ricci-flat Kahler target spaces in terms of the Hodge structure of the target space, extending an earlier observation by G. Moore. We refined this idea and obtained a conjectural statement on necessary and sufficient conditions for such SCFTs to be rational, which we indeed prove to be true in the case the target space is T^4. In the refined statement, the algebraicity of the geometric data of the target space turns out to be essential, and the Strominger--Yau--Zaslow fibration in the mirror correspondence also plays a vital role. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_00861 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Notes on Characterizations of 2d Rational SCFTs: Algebraicity, Mirror Symmetry and Complex Multiplication Kidambi, Abhiram Okada, Masaki Watari, Taizan High Energy Physics - Theory These notes combine results from two papers by the present authors viz., Part I (arXiv:2205.10299) and Part II (arXiv:2212.13028) into one streamlined version for better readability, along with a review on theory of complex multiplication for non-singular complex projective varieties and complex tori that is aimed at string theorists. We think that it is worth posting this edition as a separate entry in arXiv for those reasons, although this edition contains no essential progress beyond Part I and Part II. S. Gukov and C. Vafa proposed a characterization of rational N=(1,1) superconformal field theories (SCFTs) on 1+1 dimensions with Ricci-flat Kahler target spaces in terms of the Hodge structure of the target space, extending an earlier observation by G. Moore. We refined this idea and obtained a conjectural statement on necessary and sufficient conditions for such SCFTs to be rational, which we indeed prove to be true in the case the target space is T^4. In the refined statement, the algebraicity of the geometric data of the target space turns out to be essential, and the Strominger--Yau--Zaslow fibration in the mirror correspondence also plays a vital role. |
| title | Notes on Characterizations of 2d Rational SCFTs: Algebraicity, Mirror Symmetry and Complex Multiplication |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2408.00861 |