In theoretical physics in general and string theory in particular, the Kalb–Ramond field (named after Michael Kalb and Pierre Ramond),[1] also known as the Kalb–Ramond B-field[2] or Kalb–Ramond NS–NS B-field,[3] is a quantum field that transforms as a two-form, i.e., an antisymmetric tensor field with two indices.[1][4]

The adjective "NS" reflects the fact that in the RNS formalism, these fields appear in the NS–NS 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 Neveu–Schwarz boundary conditions) and the fields that satisfy them in 1971.[5]

The Kalb–Ramond 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 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

Curtright field
p-form electrodynamics
Ramond–Ramond field


Kalb, Michael; Ramond, P. (1974-04-15). "Classical direct interstring action". Physical Review D. American Physical Society (APS). 9 (8): 2273–2284. doi:10.1103/physrevd.9.2273. ISSN 0556-2821.
Losev, Andrei S.; Marshakov, Andrei; Zeitlin, Anton M. (2006). "On first-order formalism in string theory". Physics Letters B. Elsevier BV. 633 (2–3): 375–381. arXiv:hep-th/0510065. doi:10.1016/j.physletb.2005.12.010. ISSN 0370-2693.
Gaona, Alejandro; García, J. Antonio (2007-02-10). "First-order Actions and Duality". International Journal of Modern Physics A. World Scientific Pub Co Pte Lt. 22 (04): 851–867. arXiv:hep-th/0610022. doi:10.1142/s0217751x07034386. ISSN 0217-751X.
See also: Ogievetsky V. I., Polubarinov I. V. (1967). Sov. J. Nucl. Phys. 4. 156 (Yad. Fiz 4, 216).

Neveu, A.; Schwarz, J.H. (1971). "Tachyon-free dual model with a positive-intercept trajectory". Physics Letters B. Elsevier BV. 34 (6): 517–518. doi:10.1016/0370-2693(71)90669-1. ISSN 0370-2693.


String theory

Strings History of string theory
First superstring revolution Second superstring revolution String theory landscape



Nambu–Goto action Polyakov action Bosonic string theory Superstring theory
Type I string Type II string
Type IIA string Type IIB string Heterotic string N=2 superstring F-theory String field theory Matrix string theory Non-critical string theory Non-linear sigma model Tachyon condensation RNS formalism GS formalism

String duality

T-duality S-duality U-duality Montonen–Olive duality

Particles and fields

Graviton Dilaton Tachyon Ramond–Ramond field Kalb–Ramond field Magnetic monopole Dual graviton Dual photon


D-brane NS5-brane M2-brane M5-brane S-brane Black brane Black holes Black string Brane cosmology Quiver diagram Hanany–Witten transition

Conformal field theory

Virasoro algebra Mirror symmetry Conformal anomaly Conformal algebra Superconformal algebra Vertex operator algebra Loop algebra Kac–Moody algebra Wess–Zumino–Witten model

Gauge theory

Anomalies Instantons Chern–Simons form Bogomol'nyi–Prasad–Sommerfield bound Exceptional Lie groups (G2, F4, E6, E7, E8) ADE classification Dirac string p-form electrodynamics


Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold Ricci-flat manifold
Calabi–Yau manifold Hyperkähler manifold
K3 surface G2 manifold Spin(7)-manifold Generalized complex manifold Orbifold Conifold Orientifold Moduli space Hořava–Witten domain wall K-theory (physics) Twisted K-theory


Supergravity Superspace Lie superalgebra Lie supergroup


Holographic principle AdS/CFT correspondence


Matrix theory Introduction to M-theory

String theorists

Aganagić Arkani-Hamed Atiyah Banks Berenstein Bousso Cleaver Curtright Dijkgraaf Distler Douglas Duff Ferrara Fischler Friedan Gates Gliozzi Gopakumar Green Greene Gross Gubser Gukov Guth Hanson Harvey Hořava Gibbons Kachru Kaku Kallosh Kaluza Kapustin Klebanov Knizhnik Kontsevich Klein Linde Maldacena Mandelstam Marolf Martinec Minwalla Moore Motl Mukhi Myers Nanopoulos Năstase Nekrasov Neveu Nielsen van Nieuwenhuizen Novikov Olive Ooguri Ovrut Polchinski Polyakov Rajaraman Ramond Randall Randjbar-Daemi Roček Rohm Scherk Schwarz Seiberg Sen Shenker Siegel Silverstein Sơn Staudacher Steinhardt Strominger Sundrum Susskind 't Hooft Townsend Trivedi Turok Vafa Veneziano Verlinde Verlinde Wess Witten Yau Yoneya Zamolodchikov Zamolodchikov Zaslow Zumino Zwiebach

Physics Encyclopedia



Hellenica World - Scientific Library

Retrieved from ""
All text is available under the terms of the GNU Free Documentation License