Feynman diagrams and $Ω$-deformed M-theory

Abstract

We derive the simplest commutation relations of operator algebras associated to M2 branes and an M5 brane in the \OmegaΩ-deformed M-theory, which is a natural set-up for Twisted holography. Feynman diagram 1-loop computations in the twisted-holographic dual side reproduce the same algebraic relations.

Twisted holography of defect fusions

“…The Coulomb branch algebra of the 3d N = 4 theory is known to be 1-shifted affine g l(1) Yangian [24] and it inherits the triality property of affine g l(1) Yangian [23]. On the other hand, one can directly compute the commutator of the Higgs branch algebra and show the above is correct [9]. With the seed relations shown in (11), one can recursively find all other commutation relations for a general pair of elements in A [10].…”

“…Most of the material in this section is already known and discussed in detail in many other references. We will try to collect all necessary backgrounds here for completeness; however, for more details we direct the reader to [3,4,7,9,11]. By the Ω-deformed M-theory, we refer to 11-dimensional supergravity, which is topological in 7 directions and holomorphic in 4 directions.…”

“…Twisted holography has a nice feature that we can compare the operator algebras on each side of the duality and construct an isomorphism between two operator algebras. Moreover, demanding gauge-invariant couplings between the 5d Chern-Simons theory and the worldvolume theory of each membrane, we can derive the operator algebra of the field theory on the membrane by analyzing a certain collection of Feynman diagrams [4,9]. In other words, the…”

“…The authors discussed an OPE between two Wilson lines and show that it gives a composite Wilson line. We will sometimes rely on our previous paper [9], as well.…”

“…Twisted holography [1][2][3][4][5][6][7][8][9][10][11] 1 is a new and intriguing subject. Applying the familiar notion of a topological twist [12,13] and an Omega background [19][20][21][22] of a supersymmetric quantum field theory on the dual supergravity, we can match the protected sub-sector of the field theory and the supergravity.…”