Commutation relations for surface operators in six-dimensional (2, 0) theory

TL;DR

This paper proposes and verifies commutation relations for surface operators in the six-dimensional (2, 0) theory, connecting them to known relations in four-dimensional super Yang-Mills theory upon compactification.

Contribution

It introduces a natural guess for the commutation relations of surface operators in (2, 0) theory and verifies them at a generic moduli space point.

Findings

The proposed relations reduce to known Wilson-'t Hooft line relations in 4D.

Verification is performed considering light degrees of freedom in the moduli space.

The work links surface operators in 6D to line operators in 4D theories.

Abstract

The A_{N - 1} (2, 0) superconformal theory has an observable associated with every two-cycle in six dimensions. We make a natural guess for the commutation relations of these operators, which reduces to the commutation relations of Wilson and 't Hooft lines in four-dimensional SU(N) N = 4 super Yang-Mills theory upon compactification on a two-torus. We then verify these commutation relations by considering the theory at a generic point of its moduli space and including in the surface operators only contributions from the light degrees of freedom, which amount to N - 1 (2, 0) tensor multiplets.