A Physical Origin for Singular Support Conditions in Geometric Langlands Theory
| Autor: | Elliott, Chris, Yoo, Philsang |
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| Rok vydání: | 2017 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s00220-019-03438-z |
| Popis: | We explain how the nilpotent singular support condition introduced into the geometric Langlands conjecture by Arinkin and Gaitsgory arises naturally from the point of view of N = 4 supersymmetric gauge theory. We define what it means in topological quantum field theory to restrict a category of boundary conditions to the full subcategory of objects compatible with a fixed choice of vacuum, both in functorial field theory and in the language of factorization algebras. For B-twisted N = 4 gauge theory with gauge group G, the moduli space of vacua is equivalent to h*/W , and the nilpotent singular support condition arises by restricting to the vacuum 0 in h*/W. We then investigate the categories obtained by restricting to points in larger strata, and conjecture that these categories are equivalent to the geometric Langlands categories with gauge symmetry broken to a Levi subgroup, and furthermore that by assembling such for the groups GL_n for all positive integers n one finds a hidden factorization structure for the geometric Langlands theory. Comment: 55 pages, 5 figures, more improvements to the exposition |
| Databáze: | arXiv |
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