1branes

1branes, or 1-branes, are one-dimensional extended objects in theories that describe fundamental building blocks of matter and spacetime, such as string theory. A p-brane is an object with p spatial dimensions; therefore a 1-brane has one spatial dimension, i.e., it is a string. In string theory, 1-branes appear in two broad forms: fundamental strings, which are the basic excitations of the theory, and D1-branes, which are D-branes carrying Ramond-Ramond charge and on which open strings can end. Closed 1-branes form loops, while open 1-branes typically have endpoints constrained to lie on higher-dimensional branes.

The dynamics of a 1-brane are described by a two-dimensional worldsheet swept out in spacetime. The classical action is the Nambu-Goto action, proportional to the area of the worldsheet, or the Polyakov action, which is equivalent after gauge fixing. The energy per unit length, or tension, sets the scale of the brane; for fundamental strings the tension is T_F = 1/(2π α'), with α' the string length squared. D1-branes have tension T_D1 = 1/(2π α' g_s), where g_s is the string coupling. In Type IIB string theory there exist bound states called (p,q)-strings, with tension T_(p,q) = T_F sqrt(p^2 + (q/g_s)^2), representing composites of F-strings and D-strings.

1branes play a central role in non-perturbative aspects of string theory and in brane-based constructions of gauge theories. They participate in dualities, such as S-duality, which relates fundamental strings to D1-branes, and appear in holographic contexts where strings and branes probe curved spacetimes.