Bosonic Symmetries of $(2,0)$ DLCQ Field Theories

TL;DR

This paper explores the symmetries of a reduced six-dimensional $(2,0)$ theory derived from M-theory, revealing a rich structure of supersymmetries and conformal symmetries consistent with holographic duality.

Contribution

It identifies and characterizes the full symmetry group of the boundary theory, including boost-like and conformal symmetries, confirming the $SU(3,1)$ structure in a holographic setting.

Findings

Boundary theory has 24 supercharges.

The theory exhibits Lifshitz scaling symmetry.

The combined symmetries form a representation of $SU(3,1)$.

Abstract

We investigate symmetries of the six-dimensional $(2,0)$ theory reduced along a compact null direction. The action for this theory was deduced by considering M-theory on $AdS_7 \times S^4$ and reducing the $AdS_7$ factor along a time-like Hopf fibration which breaks one quarter of the supersymmetry and reduces the isometry group from $SO(6,2)$ to $SU(3,1)$. The boundary theory was previously shown to have 24 supercharges and a Lifshitz scaling symmetry. In this paper, we show that it has four boost-like symmetries and an additional conformal symmetry which furnish a representation of $SU(3,1)$ when combined with the other bosonic symmetries, providing a nontrivial check of the holographic correspondence.