The Kalb–Ramond field is an antisymmetric two-form background coupled to the oriented worldsheet area element. Its gauge-invariant field strength is the three-form .
When is invertible, choose . Residual gauge parameters are exact one-forms and act trivially on . The remaining independent modes are antisymmetric transverse components , satisfying ; longitudinal components obey . There are physical polarizations.
The three-form field strength of the Kalb–Ramond field is . Its components are . In flat spacetime the free equation is .
The H-field is the three-form field strength of a Kalb–Ramond field. It obeys the Bianchi identity and contributes quadratically to the leading string background equations.
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The Kalb-Ramond field is a theoretical construct in physics, specifically in the context of string theory and higher-dimensional field theories. It is a type of antisymmetric tensor field, typically denoted as \( B_{\mu\nu} \), where the indices \( \mu \) and \( \nu \) represent spacetime dimensions.