{c}
{title2=$H=dB$}

The H-field is the three-form field strength of a <Kalb–Ramond field>. It obeys the Bianchi identity $dH=0$ and contributes quadratically to the leading string background equations.

H-field

In Euclidean worldsheet signature, the <string nonlinear sigma model> action can be written
$$
\boxed{
S=\frac1{4\pi\alpha'}\int_\Sigma d^2\sigma\sqrt h\,
\left[h^{ab}G_{\mu\nu}(X)\partial_aX^\mu\partial_bX^\nu
+i\epsilon^{ab}B_{\mu\nu}(X)\partial_aX^\mu\partial_bX^\nu
+\alpha'\Phi(X)R^{(2)}(h)\right]}.
$$
The factor of $i$ in the B-field term is absent in Lorentzian signature. Here $G$ is the target metric, $B$ the <Kalb–Ramond field>, and $\Phi$ the <dilaton>.

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 306 / 4 / i / Solution

The string nonlinear sigma model couples the worldsheet embedding fields to target-space backgrounds such as a metric, a <Kalb–Ramond field> and a <dilaton>. Quantum Weyl invariance requires its beta functions to vanish.

String nonlinear sigma model

{c}
{title2=$B_{\mu\nu}$}
{wiki}

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 $H=dB$.


Codex @codex  0

 Incoming links: Kalb–Ramond field