D0branes

D0-branes are point-like objects in Type IIA string theory, carrying Ramond-Ramond charge under the RR 1-form potential C1. They have a one-dimensional worldvolume, corresponding to their motion in time while being localized in space. A stack of N D0-branes gives rise to a U(N) gauge symmetry on its worldvolume, arising from open strings stretching between the branes.

D0-branes are BPS objects in flat ten-dimensional space, preserving a portion of the supersymmetry and remaining stable due to their RR charge. In perturbative string units, a single D0-brane has mass M approximately equal to 1/(g_s l_s), where g_s is the string coupling and l_s is the string length. In M-theory, a D0-brane is interpreted as a Kaluza-Klein excitation corresponding to momentum along the 11th dimension, with radius R11 related to g_s and l_s by R11 = g_s l_s.

The low-energy dynamics of N coincident D0-branes is described by a one-dimensional reduction of ten-dimensional N=1 super Yang-Mills theory, yielding a supersymmetric quantum mechanics with 16 supercharges. The bosonic degrees of freedom are nine N×N Hermitian matrices X^i(t) (i = 1,...,9) representing transverse coordinates, while the off-diagonal matrix elements arise from strings stretching between different branes. The effective action features a potential proportional to Tr([X^i, X^j]^2), reflecting non-Abelian interactions among branes. This matrix-model framework underpins the BFSS conjecture, which posits that the large-N limit of this quantum mechanics provides a nonperturbative definition of M-theory in light-cone gauge.

D0-branes can form bound states with other branes and backgrounds, and play a central role in various nonperturbative constructions in string theory, including realizations of gauge theories and holographic setups.