Some remarks on the index theorem approach to anomalies

Maurizio Martellini; Cesare Reina

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The author constructs the gauged Skyrme model by introducing the skyrmion bundle as follows: instead of considering maps $U : M \to {SU}_{N_{F}}$ he thinks of the meson fields as of global sections in a bundle $B (M, {SU}_{N_{F}}, G) = P (M, G) \times_{G} {SU}_{N_{F}}$ . 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 $N_{F} \leq 6$ , one has $H^{*} (E G \times_{G} {SU}_{N_{F}}) ≅ H^{*} {({SU}_{N_{F}})}^{G} ≅ S ({\underset{̲}{G}}^{*}) \otimes H^{*} ({SU}_{N_{F}}) ≅ H^{*} (B G) \otimes H^{*} ({SU}_{N_{F}}),$ where $E G (B G, G)$ is the universal...