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Title: Equivariant cohomology of the skyrmion bundle (English)
Author: Gross, Christian
Language: English
Journal: Proceedings of the 16th Winter School "Geometry and Physics"
Issue: 1996
Pages: [87]-96
Category: math
Summary: 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 $N_F\leq 6$, one has $$ H^{*}(EG\times_G \text{SU}_{N_F})\cong H^{*}(\text{SU}_{N_F})^G \cong \text{S}({\underline G}^{*})\otimes H^{*}(\text{SU}_{N_F}) \cong H^{*}(BG)\otimes H^{*}(\text{SU}_{N_F}), $$ where $EG(BG,G)$ is the universal bundle for the Lie group $G$ and $\underline G$ is the Lie algebra of $G$. (English)
MSC: 53C80
MSC: 53Z05
MSC: 55N91
MSC: 55R91
MSC: 58A12
MSC: 81V05
idZBL: Zbl 0905.53052
idMR: MR1469024
Date available: 2009-07-13T21:37:53Z
Last updated: 2012-09-18
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