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
References
- ^
- ^ Also see: Ogievetsky V. I., Polubarinov I. V. (1967). Sov. J. Nucl. Phys. 4. 156 (Yad. Fiz 4, 216)