Kalb–Ramond field

In theoretical physics in general and string theory in particular, the Kalb–Ramond field, also known as the NS-NS B-field, is a quantum field that transforms as a two-form i.e. an antisymmetric tensor field with two indices.^[1][2]

It generalizes the electromagnetic potential but it has two indices instead of one. This difference is related to the fact that the electromagnetic potential is integrated over one-dimensional worldlines of particles to obtain one of its contributions to the action while the Kalb–Ramond field must be integrated over the two-dimensional worldsheet of the string. In particular, while the action for a charged particle moving in an electromagnetic potential is given by

$-q\int dx^\mu A_\mu$

that for a string coupled to the Kalb–Ramond field has the form

$-\int dx^\mu dx^\nu B_{\mu\nu}$

This term in the action implies that the fundamental string of string theory is a source of the NS-NS B-field, much like charged particles are sources of the electromagnetic field.

The Kalb–Ramond field appears, together with the metric tensor and dilaton, as a set of massless excitations of a closed string.

See also

• p-form electrodynamics
• Curtright field

References

1. Michael Kalb and P. Ramond (1974). "Classical direct interstring action". Phys. Rev. D 9 (8): 2273–2284. Bibcode:1974PhRvD...9.2273K. doi:10.1103/PhysRevD.9.2273.
2. Also see: Ogievetsky V. I., Polubarinov I. V. (1967). Sov. J. Nucl. Phys. 4. 156 (Yad. Fiz 4, 216)