(2,0) Tensor Multiplets and Conformal Supergravity in D=6

TL;DR

The authors formulate six-dimensional $(2,0)$ supergravity in a conformal framework by constructing the $(2,0)$ supercurrent multiplet from the tensor multiplet, gauging the superconformal algebra $OSp(8^*|4)$ to obtain nonlinear Weyl multiplet transformations, and deriving the full tensor-multiplet equations of motion in a conformal supergravity background. They then realize $(2,0)$ Poincaré supergravity coupled to $N$ tensor multiplets by introducing $N+5$ tensor multiplets with a geometric scalar constraint that fixes conformal symmetry, resulting in scalars parametrizing the coset $SO(N,5)/(SO(N) imes SO(5))$. This conformal-calculus framework reproduces known Poincaré results upon gauge fixing and provides a natural setting for studying the boundary theory in AdS$_7$/CFT$_6$, with prospects for higher-spin extensions and M5-brane couplings. The work thus supplies a comprehensive, off-shell-compatible construction of $(2,0)$ dynamics in a conformal background and a path to boundary correlator analyses in holography.

Abstract

We construct the supercurrent multiplet that contains the energy-momentum tensor of the (2,0) tensor multiplet. By coupling this multiplet of currents to the fields of conformal supergravity, we first construct the linearized superconformal transformations rules of the (2,0) Weyl multiplet. Next, we construct the full non-linear transformation rules by gauging the superconformal algebra OSp(8^*|4). We then use this result to construct the full equations of motion of the tensor multiplet in a conformal supergravity background. Coupling N+5 copies of the tensor multiplet to conformal supergravity and imposing a geometrical constraint on the scalar fields which fixes the conformal symmetry, we obtain the coupling of (2,0) Poincare supergravity to N tensor multiplets in which the physical scalars parametrize the coset SO(N,5)/(SO(N) x SO(5)).