A domain wall in twisted M-theory

Abstract

We study a four-dimensional domain wall in twisted M-theory. The domain wall is engineered by intersecting D6 branes in the type IIA frame. We identify the classical algebra of operators on the domain wall in terms of a higher vertex operator algebra, which describes the holomorphic subsector of a 4d \mathcal{N}=1𝒩=1 supersymmetric field theory, and compute the associated mode algebra. We conjecture that the quantum deformation of the classical algebra is isomorphic to the bulk algebra of operators from which we establish twisted holography of the domain wall.

Evidence for an algebra of G2 instantons

“…Exploiting such quantum mechanics it is the key towards understanding the algebra of G 2 instantons for the example we consider, in particular, zooming to the intersection point of a pair of associatives, one has a local model that can be traced back to a well-known orbifold of the Bryant-Salamon metric for the G 2 cone over the three-dimensional complex projective plane CP 3 [56], that were discussed in [57,58]. This is a universal building block for the G 2 instanton partition functions that can be understood in terms of the twisted M-theory à la Costello [30] (see also [32,33]), along the lines of [60].…”

“…Note that there is a supersymmetric constraint on θ of each L θ and there is Omega deformation turned on L θ . The compatibility with Omega background and supersymmetric constraint was discussed in [60].…”

Towards the Finite-$N$ Twisted Holography from the Geometry of Phase Space

“…Recently, a twisted version of The AdS/CFT Correspondence has been formulated by Costello [4,5]. According to this framework, the holography can be understood as certain algebraic relation, known as Koszul duality, between the algebra of operators in the two sides of the correspondence (see [6] for an earlier example and also [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] for follow-up and related works). For a recent and very readable review of Koszul duality aimed at physicists, we refer the reader to [23].…”