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Chern-Simons in the Seiberg-Witten map for non-commutative Abelian gauge theories in 4D | | Marco Picariello
; Andrea Quadri
; Silvio P. Sorella
; | | Date: |
10 Oct 2001 | | Journal: | JHEP 0201 (2002) 045 | | Subject: | hep-th | | Affiliation: | Universita` di Milano, Universidade do Estado do Rio de Janeiro | | Abstract: | A cohomological BRST characterization of the Seiberg-Witten (SW) map is given. We prove that the coefficients of the SW map can be identified with elements of the cohomology of the BRST operator modulo a total derivative. As an example, it will be illustrated how the first coefficients of the SW map can be written in terms of the Chern-Simons three form. This suggests a deep topological and geometrical origin of the SW map. The existence of the map for both Abelian and non-Abelian case is discussed. By using a recursive argument and the associativity of the $star$-product, we shall be able to prove that the Wess-Zumino consistency condition for non-commutative BRST transformations is fulfilled. The recipe of obtaining an explicit solution by use of the homotopy operator is briefly reviewed in the Abelian case. | | Source: | arXiv, hep-th/0110101 | | Services: | Forum | Review | PDF | Favorites | |
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