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24.03.2021 (Wednesday)

Protected operator algebras and holography

Regular Seminar Connor Behan (Oxford)

14:00 IC
room Zoom

Bootstrap methods have greatly expanded our ability to compute correlation functions in the supergravity approximation. As a result, we now know Mellin space expressions for general half-BPS four-point functions at tree-level in the main holographic CFTs with maximal supersymmetry. These are the $\mathcal{N} = (2,0)$ theory in six dimensions, $\mathcal{N} = 4$ Super Yang Mills in four dimensions and $\mathcal{N} = 8$ ABJM theory in three dimensions. In all three cases, a rich subsector of operators that generate an infinite dimensional symmetry may be constructed by passing to the cohomology of a certain nilpotent supercharge. I will explain the main features of this construction and how they may be accessed holographically. When the protected operators generate a W-algebra, we will see that their four-point functions agree precisely with those predicted by AdS / CFT thus giving a complete check. The other possibility leads us to consider topological quantum mechanics where the calculations are more difficult. Nevertheless, I will show that an infinite family of special OPE coefficients obeys non-perturbative relations that follow from the one-dimensional theory.