M2-brane surface operators and gauge theory dualities in Toda
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arXiv
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| Format: | Preprint |
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2014
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| _version_ | 1866911736805720064 |
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| author | Gomis, Jaume Floch, Bruno Le |
| author_facet | Gomis, Jaume Floch, Bruno Le |
| contents | We give a microscopic two dimensional ${\cal N}=(2,2)$ gauge theory description of arbitrary M2-branes ending on $N_f$ M5-branes wrapping a punctured Riemann surface. These realize surface operators in four dimensional ${\cal N}=2$ field theories. We show that the expectation value of these surface operators on the sphere is captured by a Toda CFT correlation function in the presence of an additional degenerate vertex operator labelled by a representation ${\cal R}$ of $SU(N_f)$, which also labels M2-branes ending on M5-branes. We prove that symmetries of Toda CFT correlators provide a geometric realization of dualities between two dimensional gauge theories, including ${\cal N}=(2,2)$ analogues of Seiberg and Kutasov--Schwimmer dualities. As a bonus, we find new explicit conformal blocks, braiding matrices, and fusion rules in Toda CFT. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1407_1852 |
| institution | arXiv |
| publishDate | 2014 |
| record_format | arxiv |
| spellingShingle | M2-brane surface operators and gauge theory dualities in Toda Gomis, Jaume Floch, Bruno Le High Energy Physics - Theory We give a microscopic two dimensional ${\cal N}=(2,2)$ gauge theory description of arbitrary M2-branes ending on $N_f$ M5-branes wrapping a punctured Riemann surface. These realize surface operators in four dimensional ${\cal N}=2$ field theories. We show that the expectation value of these surface operators on the sphere is captured by a Toda CFT correlation function in the presence of an additional degenerate vertex operator labelled by a representation ${\cal R}$ of $SU(N_f)$, which also labels M2-branes ending on M5-branes. We prove that symmetries of Toda CFT correlators provide a geometric realization of dualities between two dimensional gauge theories, including ${\cal N}=(2,2)$ analogues of Seiberg and Kutasov--Schwimmer dualities. As a bonus, we find new explicit conformal blocks, braiding matrices, and fusion rules in Toda CFT. |
| title | M2-brane surface operators and gauge theory dualities in Toda |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/1407.1852 |