D0brane

A D0-brane is a point-like object in Type II string theory that carries Ramond-Ramond charge under the RR one-form potential C1. As a D-brane with zero spatial dimensions, it is localized in all spatial directions and extends only along the time direction of its worldvolume. A single D0-brane is a fundamental source for the RR field associated with C1 and interacts with other D-branes and strings through open string modes that end on it.

The D0-brane has a tension and mass that scale with the string coupling as M ~ 1/(g_s l_s), where l_s is the string length and g_s is the string coupling. This makes it a heavy, non-perturbative object at weak coupling but connects to perturbative descriptions in certain limits. D0-branes can be BPS states, preserving a portion of the supersymmetry when at rest, which stabilizes their mass and charge balance.

In M-theory, the D0-brane of Type IIA string theory corresponds to Kaluza-Klein momentum along the 11th dimension when M-theory is compactified on a circle of radius R_11. The relation R_11 ∝ g_s l_s links the D0-brane’s properties to the geometry of the extra dimension, and its KK momentum interpretation provides a bridge between Type IIA string theory and 11-dimensional supergravity.

Matrix theory offers a non-perturbative description of multiple D0-branes: the N D0-branes are governed by a 0+1 dimensional U(N) super Yang-Mills theory, with the transverse positions promoted to N×N matrices. This Matrix Theory, in the BFSS framework, is proposed as a microscopic formulation of M-theory in a particular light-cone frame, where the dynamics of D0-branes encode the degrees of freedom of spacetime and gravity at high energies.

D0-branes thus play a central role in string theory’s non-perturbative structure, dualities, and approaches to quantum gravity.