Structure of the $\mathcal{N}=4$ chiral algebra

TL;DR

This paper investigates the structure of the $ ext{N}=4$ superconformal vertex operator algebra associated with 4D $ ext{N}=4$ SU$(N)$ super-Yang-Mills theory, revealing its unique characterization by the central charge and implications for its origin.

Contribution

It provides a recursive analysis of the algebra's constraints, showing it is uniquely determined by the central charge without extra parameters.

Findings

The algebra is uniquely characterized by the central charge.

It cannot originate from the symmetric orbifold.

The structure is constrained by associativity of the OPE.

Abstract

The chiral algebra of 4D $\mathcal{N}=4$ SU$(N)$ super-Yang-Mills theory is an $\mathcal{N}=4$ superconformal vertex operator algebra. We analyse the structure of this algebra by studying recursively the constraints that are required by the associativity of the operator product expansion. We find that the algebra is uniquely characterized by the central charge (which can take an arbitrary value), without any additional free parameter. Furthermore, the truncation pattern of the OPE coefficients suggests that the algebra cannot arise from the symmetric orbifold.