QFT In the literature: open

Intrinsic definition of the six-dimensional (2,0) theory

In plain words

The six-dimensional $(2,0)$ theory, the version with the maximum amount of supersymmetry, is defined only as a limit of a stack of M5-branes, membrane-like objects of M-theory. A definition that stands on its own is missing.

Precise statement

The 6D $N=(2,0)$ superconformal theory of type $A_{N-1}$ is defined as the low-energy limit of N coincident M5-branes or of type IIB string theory on $C^2/Z_N$. Give a self-contained definition independent of string and M-theory (operator algebra and Hilbert space, a UV completion via 5D maximally supersymmetric Yang-Mills, deconstruction, or a lattice limit) that reproduces known data: anomaly coefficients scaling as $N^3$, the $W_N$ chiral algebra, and the protected spectrum.

What would settle it

A construction from which the $N^{3}$ anomaly scaling and the $W_N$ chiral algebra follow as derived results.

Status in the literature

Proposals that 5D maximally supersymmetric Yang-Mills is a complete definition (2010-2011) and deconstruction approaches are not accepted as complete.