Holography and Koszul duality: the example of the $M2$ brane

Understand

Si Li and author suggested in that, in some cases, the AdS/CFT correspondence can be formulated in terms of the algebraic operation of Koszul duality.

• In this paper this suggestion is checked explicitly for $M2$ branes in an $\Omega$-background.
• The algebra of supersymmetric operators on a stack of $K$ $M2$ branes is shown to be Koszul dual, in large $K$, to the algebra of supersymmetric operators of $11$-dimensional supergravity in an $\Omega$-background (using the formulation of supergravity in an $\Omega$-background presented in arXiv:1610.04144).
• The twisted form of supergravity that is used here can be quantized to all orders in perturbation theory.