Kalb-Ramond field

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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.

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 d\tau {dx^\mu\over d\tau} A_\mu

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

-\int d\tau d\sigma {\partial x^\mu\over \partial\tau} {\partial x^\nu\over \partial\sigma} 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

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