Canonical charges and central extension of the null-reduced theory

Determine whether the higher Galilean conformal modes of the null-reduced Galilean Kalb–Ramond action are recovered as canonical Noether charges with a central term, while fixing the physical degree-of-freedom count through the Hamiltonian analysis of its reducible gauge symmetry and Dirac brackets.

Background

The null-reduction construction produces the local Galilean Kalb–Ramond action with fields $\chi$, $\psi_i$, $E_i$, and $B_{ij}$, but the action is invariant only under the global Galilean generators and not under the higher modes of the infinite-dimensional Galilean conformal algebra. The paper identifies a Hamiltonian analysis as the next step for understanding whether those non-invariant higher modes nevertheless act as phase-space charges, potentially with a central extension.

Because the Kalb–Ramond gauge symmetry is reducible, the proposed analysis must also account for the associated gauge-for-gauge structure when determining the physical degrees of freedom and constructing the Dirac brackets and Noether-charge algebra.