Hamiltonian derivation of dual gravitational charges

TL;DR

This paper derives dual gravitational charges using Hamiltonian methods in the first order formalism, incorporating the Holst and Nieh-Yan terms, and constructs their algebra.

Contribution

It introduces a Hamiltonian derivation of dual BMS charges with a new method for computing integrable dual charges and their algebra.

Findings

Derived dual BMS charges using Hamiltonian formalism.

Constructed the algebra of dual charges.

Identified the role of the Nieh-Yan term with fermions.

Abstract

We provide a Hamiltonian derivation of recently discovered dual BMS charges. In order to do so, we work in the first order formalism and add to the usual Palatini action, the Holst term, which does not contribute to the equations of motion. We give a method for finding the leading order integrable dual charges \`a la Wald-Zoupas and construct the corresponding charge algebra. We argue that in the presence of fermions, the relevant term that leads to dual charges is the topological Nieh-Yan term.