Tensor Multiplets in Six-Dimensional (2,0) Supergravity

TL;DR

The paper addresses constructing the complete coupling of six-dimensional $ (2,0) $ supergravity to an arbitrary number of tensor multiplets, including all fermionic terms. It develops a non-linear, supercovariant formulation built on the scalar coset $SO(5,n)/SO(5)\times SO(n)$, with supercovariant field strengths $\hat{H}^r_{\mu\nu\rho}$ and $\hat{\cal H}^r_{\mu\nu\rho}$ that satisfy (anti)self-duality, and derives the full fermionic equations and SUSY transformations. A key result is the on-shell closure of the full $ (2,0) $ supersymmetry algebra and the complete Lagrangian consistent with tensor self-duality and the gauge structure, including higher-order fermionic corrections. The work also shows that truncation to $ (1,0) $ supergravity with $n$ tensor multiplets precisely reduces to the known $ (1,0) $ results, confirming consistency with prior analyses and enabling a seamless connection to related flatspace limits and string compactifications on $K3$ that yield these six-dimensional theories.

Abstract

We construct the complete coupling of $(2,0)$ supergravity in six dimensions to $n$ tensor multiplets, extending previous results to all orders in the fermi fields. The truncation to $(1,0)$ supergravity coupled to tensor multiplets exactly reproduces the complete couplings recently obtained.