# 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.[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

${\displaystyle -q\int dx^{\mu }A_{\mu }}$

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

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

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.