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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
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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.

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Marco Picariello, Andrea Quadri, Silvio P. Sorella. 2001-10-10. Chern-Simons in the Seiberg-Witten map for non-commutative Abelian gauge theories in 4D. https://doi.org/10.1088/1126-6708%2F2002%2F01%2F045

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