In theoretical physics in general and string theory in particular, the KalbâÂÂRamond field (named after Michael Kalb and Pierre Ramond), also known as the KalbâÂÂRamond B-field or KalbâÂÂRamond NSâÂÂNS B-field, is a quantum field that transforms as a two-form, i.e., an antisymmetric tensor field with two indices.
The adjective "NS" reflects the fact that in the RNS formalism, these fields appear in the NSâÂÂNS sector in which all vector fermions are anti-periodic. Both uses of the word "NS" refer to André Neveu and John Henry Schwarz, who studied such boundary conditions (the so-called NeveuâÂÂSchwarz boundary conditions) and the fields that satisfy them in 1971.
The KalbâÂÂRamond field 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 KalbâÂÂRamond 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
that for a string coupled to the KalbâÂÂRamond field has the form
This term in the action implies that the fundamental string of string theory is a source of the NSâÂÂNS B-field, much like charged particles are sources of the electromagnetic field.
The KalbâÂÂRamond field appears, together with the metric tensor and dilaton, as a set of massless excitations of a closed string.