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.
Highlights
(const)ε1ε22 t[0, 0]t[0, 0]∂z21 ∂z2 A1∂z11 ∂z22 c2. This indicates that the theory is quantum mechanically inconsistent, as it has a Feynman diagram that has nonzero BRST variation
We studied the simplest possible configurations of M2 and M5 branes in the Ω−deformed and topologically twisted M-theory
We showed the operator algebra living on the M2 branes acts on the operator algebra on M5 brane, and computed the
Summary
In [1], Costello and Li developed a beautiful formalism, which prescribes a way to topologically twist supergravity. In the presence of the topological defect that couples the 1d TQM and the 5d CS theory, certain Feynman diagrams turn out to have non-zero BRST variations. For the combined, interacting theory to be quantum mechanically consistent, the BRST variations of the Feynman diagrams should combine to give zero. This procedure magically reproduces the algebra commutation relations that define 1d TQM operator algebra, Aε1,ε2. The commutator of the simplest bi-module Mε1,ε2 of Aε1,ε2 , which has ε1 correction This will be solved by two complementary ways: 2The actual computation in [18] is more subtle, and will not be used in this work. We are curious if our story can be further generalized to the coupled system of the 5d U(1) CS theory and the generalized W1+∞ algebra
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