2 changed the words "action/Lagrangian" to "term"

Does anyone have a reference to learn more about the Cartan $3$-form on a group manifold $G$? I have read that the WZW Lagrangian term is nothing more than the integral of the pullback of the Cartan $3$-form via $g:W\rightarrow G$

$WZW = -\frac{1}{6}\int_W \langle \phi_g\wedge[\phi_g\wedge\phi_g]\rangle$,

where $\phi_g=g^\ast(\phi)$ is the pullback of the Maurer-Cartan form, and would like to learn more about the math behind WZW actionsterms. For eg., why is it the generator of $H^3(G,\mathbb{R})$ when $G$ is a connected, simply connected, compact Lie group?

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# Cartan 3-form on a Lie group G

Does anyone have a reference to learn more about the Cartan $3$-form on a group manifold $G$? I have read that the WZW Lagrangian is nothing more than the integral of the pullback of the Cartan $3$-form via $g:W\rightarrow G$

$WZW = -\frac{1}{6}\int_W \langle \phi_g\wedge[\phi_g\wedge\phi_g]\rangle$,

where $\phi_g=g^\ast(\phi)$ is the pullback of the Maurer-Cartan form, and would like to learn more about the math behind WZW actions. For eg., why is it the generator of $H^3(G,\mathbb{R})$ when $G$ is a connected, simply connected, compact Lie group?