0branes

0branes, also known as zero-branes or D0-branes in the context of string theory, are pointlike objects that arise as dynamical branes in type IIA string theory. They carry Ramond–Ramond one-form charge and can act as the endpoints of open strings. A system of N coincident 0branes is described at low energies by a supersymmetric quantum mechanics with U(N) gauge symmetry, obtained by dimensional reduction of ten-dimensional N=1 super-Yang–Mills theory to one time dimension.

In a single 0brane, the worldvolume theory reduces to the dynamics of a particle with supersymmetric structure. For N branes, the transverse positions are encoded in nine N by N matrix coordinates X^i, i=1,...,9. When the matrices are diagonal, the branes appear at definite positions and the moduli space corresponds to the nine-dimensional space of brane locations. Off-diagonal elements represent strings stretched between pairs of branes and become massive when branes are separated, giving rise to nontrivial interactions through the matrix degrees of freedom. The complete 0brane system is described by a quantum mechanics known as matrix quantum mechanics, which is the dimensional reduction of 10D super-Yang–Mills theory.

A central connection to M-theory is the BFSS matrix model, which posits that the quantum mechanics of N D0-branes provides a non-perturbative definition of M-theory in eleven dimensions in a particular infinite-momentum frame. In this perspective, the eleven-dimensional dimension emerges from strong coupling of type IIA string theory, with D0-branes corresponding to Kaluza–Klein excitations along the emergent direction.

0branes thus play a key role in discussions of nonperturbative string theory, dualities, and the proposed matrix-model formulation of M-theory.