Instantons and the Large N=4 Algebra
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912163559374848 |
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| author | Witten, Edward |
| author_facet | Witten, Edward |
| contents | We investigate the differential geometry of the moduli space of instantons on S^3 x S^1. Extending previous results, we show that a sigma-model with this target space can be expected to possess a large N=4 superconformal symmetry, supporting speculations that this sigma-model may be dual to Type IIB superstring theory on AdS_3 x S^3 x S^3 x S^1. The sigma-model is parametrized by three integers -- the rank of the gauge group, the instanton number, and a "level" (the integer coefficient of a topologically nontrivial B-field, analogous to a WZW level). These integers are expected to correspond to two five-brane charges and a one-brane charge. The sigma-model is weakly coupled when the level, conjecturally corresponding to one of the five-brane changes, becomes very large, keeping the other parameters fixed. The central charges of the large N=4 algebra agree, at least semiclassically, with expectations from the duality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20964 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Instantons and the Large N=4 Algebra Witten, Edward High Energy Physics - Theory We investigate the differential geometry of the moduli space of instantons on S^3 x S^1. Extending previous results, we show that a sigma-model with this target space can be expected to possess a large N=4 superconformal symmetry, supporting speculations that this sigma-model may be dual to Type IIB superstring theory on AdS_3 x S^3 x S^3 x S^1. The sigma-model is parametrized by three integers -- the rank of the gauge group, the instanton number, and a "level" (the integer coefficient of a topologically nontrivial B-field, analogous to a WZW level). These integers are expected to correspond to two five-brane charges and a one-brane charge. The sigma-model is weakly coupled when the level, conjecturally corresponding to one of the five-brane changes, becomes very large, keeping the other parameters fixed. The central charges of the large N=4 algebra agree, at least semiclassically, with expectations from the duality. |
| title | Instantons and the Large N=4 Algebra |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2407.20964 |