String Field Theory - Light-cone String Field Theory

Light-cone String Field Theory

Light-cone string field theories were introduced by Stanley Mandelstam and developed by Mandelstam, Michael Green, John Schwarz and Lars Brink. An explicit description of the second-quantization of the light-cone string was given by Michio Kaku and Keiji Kikkawa.

Light-cone string field theories were the first string field theories to be constructed and are based on the simplicity of string scattering in light-cone gauge. For example, in the bosonic closed string case, the worldsheet scattering diagrams naturally take a Feynman diagram-like form, being built from two ingredients, a propagator,

and two vertices for splitting and joining strings, which can be used to glue three propagators together,

These vertices and propagators produce a single cover of the moduli space of -point closed string scattering amplitudes so no higher order vertices are required. Similar vertices exist for the open string.

When one considers light-cone quantized superstrings, the discussion is more subtle as divergences can arise when the light-cone vertices collide. To produce a consistent theory, it is necessary to introduce higher order vertices, called contact terms, to cancel the divergences.

Light-cone string field theories have the disadvantage that they break manifest Lorentz invariance. However, in backgrounds with light-like killing vectors, they can considerably simplify the quantization of the string action. Moreover, until the advent of the Berkovits string it was the only known method for quantizing strings in the presence of Ramond–Ramond fields. In recent research, light-cone string field theory played an important role in understanding strings in pp-wave backgrounds.