Covariant Phase Space and Carroll-Weyl $χ$ Symmetry of Carroll Non-BPS D$_p$-branes

Abstract: We analyze the covariant phase space of Klusoň's canonical Carroll non-BPS D(_p)-brane actions. The Carroll limit is formulated as a contraction of the canonical phase space: the canonical one-form is invariant under the scaling of conjugate pairs, while the leading Hamiltonian constraint differs between the electric-like and magnetic-like sectors. This difference controls the weak closure of the electric-like constraint algebra and the stronger closure of the magnetic-like Hamiltonian brackets. We separate the generic non-BPS sector, which carries (D-1) local phase-space degrees of freedom, from the tachyon-vacuum sector, which carries (D-2) only after imposing second-class background conditions. We also identify the rank condition for the generic electric-like sector and its strengthening in the vacuum sector. Finally, we show that the Carroll--Weyl (χ) transformation preserves the symplectic form and admits a charge, but is obstructed by the constraints and cannot be promoted to a first-class gauge generator except in a highly restricted global vacuum sector. This contrasts with null string theory, where a restricted (χ)-symmetry can be completed to an additional first-class constraint.