M2-brane surface operators and gauge theory dualities in Toda

摘要: We give a microscopic two dimensional $$ \mathcal{N} $$ = (2, 2) gauge theory description of arbitrary M2-branes ending on N f M5-branes wrapping punctured Riemann surface. These realize surface operators in four 2 field theories. show that the expectation value these sphere is captured by Toda CFT correlation function presence an additional degenerate vertex operator labelled representation \mathrm{\mathcal{R}} SU(N ), which also labels M5-branes. prove symmetries correlators provide geometric realization dualities between theories, including analogues Seiberg and Kutasov-Schwimmer dualities. As bonus, we find new explicit conformal blocks, braiding matrices, fusion rules CFT.