The author constructs the gauged Skyrme model by introducing the skyrmion bundle as follows: instead of considering maps $U:M\to {\text{SU}}_{N_F}$ he thinks of the meson fields as of global sections in a bundle $B(M,{\text{SU}}_{N_F},G)=P(M,G){\times }_G{\text{SU}}_{N_F}$. For calculations within the skyrmion bundle the author introduces by means of the so-called equivariant cohomology an analogue of the topological charge and the Wess-Zumino term. The final result of this paper is the following Theorem. For the skyrmion bundle with $N_F\le 6$, one has $$H^{*}\left(EG{\times }_G{\text{SU}}_{N_F}\right)\cong H^{*}{\left({\text{SU}}_{N_F}\right)}^G\cong \text{S}\left({\underline{G}}^{*}\right)\otimes H^{*}\left({\text{SU}}_{N_F}\right)\cong H^{*}\left(BG\right)\otimes H^{*}\left({\text{SU}}_{N_F}\right),$$ where $EG(BG,G)$ is the universal bundle for the Lie group $G$ and $\underline{G}$ is the Lie algebra of $G$.

EUDML-ID : urn:eudml:doc:221614
Mots clés:

@article{701598,
     title = {Equivariant cohomology of the skyrmion bundle},
     booktitle = {Proceedings of the 16th Winter School "Geometry and Physics"},
     series = {GDML\_Books},
     publisher = {Circolo Matematico di Palermo},
     address = {Palermo},
     year = {1997},
     pages = {[87]-96},
     mrnumber = {MR1469024},
     zbl = {0905.53052},
     url = {http://dml.mathdoc.fr/item/701598}
}

Gross, Christian. Equivariant cohomology of the skyrmion bundle, dans Proceedings of the 16th Winter School "Geometry and Physics", GDML_Books,  (1997), pp. [87]-96. http://gdmltest.u-ga.fr/item/701598/