pbranes

In string theory and M-theory, p-branes are p-dimensional extended objects that generalize strings. They have p spatial dimensions, so their worldvolume is (p+1)-dimensional when time is included. Branes appear as dynamical objects and as classical solutions to the low-energy supergravity theories describing the massless modes of strings and membranes. They can carry charges under higher-form fields and interact with gravitons and other branes. The label p denotes the number of spatial dimensions; p=0,1,2,... include particles, strings, membranes, and higher-dimensional branes. Major families include fundamental branes, D-branes, NS-branes, and M-branes (such as M2 and M5).

The dynamics of branes depend on their type. Fundamental and solitonic branes are described by different actions: fundamental branes follow a Nambu-Goto-like action, while D-branes are described by the Dirac-Born-Infeld action with couplings to Ramond-Ramond potentials; open strings ending on D-branes yield gauge theories on the brane worldvolume. M-branes are described by covariant membrane actions in eleven dimensions. In many contexts branes preserve part of the background supersymmetry, giving BPS configurations with stable mass-charge relations.

In supergravity, p-branes appear as charged, extremal solutions with metrics that are warped products of the worldvolume and a transverse space, governed by harmonic functions in the transverse coordinates. They source the corresponding form fields and can intersect in allowed configurations. Dualities relate different brane types, exchanging charges and winding. A prominent example is the stack of D3-branes, which yields the AdS5×S5 geometry central to gauge/gravity duality; M2- and M5-branes give AdS4×S7 and AdS7×S4 in M-theory.

p-branes play a central role in modern high-energy theory, providing a non-perturbative description of gauge theories, enabling holographic dualities, and serving as building blocks for compactifications and brane constructions in phenomenology.