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

Abstract

We analyze the covariant phase space of Kluso\v{n}'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 $\chi$ transformation, the matter-sector analogue of the null-string Carroll--Weyl symmetry, 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. The obstruction is algebraic in $\chi$, so no restriction of its spacetime profile can remove it. This contrasts with null string theory, where a restricted $\chi$-symmetry can be completed to an additional first-class constraint.