Mehen, Thomas and Wise, Mark B. (2001) Generalized *-products, Wilson lines and the solution of the Seiberg-Witten equations. Journal of High Energy Physics, 2000 (12). Art. no. 008. ISSN 1126-6708. http://resolver.caltech.edu/CaltechAUTHORS:MEHjhep00
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Higher order terms in the effective action of non-commutative gauge theories exhibit generalizations of the star-product (e.g. star' and star3). These terms do not manifestly respect the non-commutative gauge invariance of the tree level action. In U(1) gauge theories, we note that these generalized star-products occur in the expansion of some quantities that are invariant under non-commutative gauge transformations, but contain an infinite number of powers of the non-commutative gauge field. One example is an open Wilson line. Another is the expression for a commutative field strength tensor Fab in terms of the non-commutative gauge field hat Aa. Seiberg and Witten derived differential equations that relate commutative and non-commutative gauge transformations, gauge fields and field strengths. In the U(1) case we solve these equations neglecting terms of fourth order in hat A but keeping all orders in the non-commutative parameter θkl.
|Additional Information:||Received 10 November 2000, accepted for publication 13 December 2000, Published 15 January 2001 We thank J. Gomis and E. Witten for useful discussions. T.M. was supported by the National Science Foundation under Grant No. PHY-9800964. M.B.W. was supported in part by the Department of Energy under grant DE-FG03-ER-40701.|
|Subject Keywords:||Nonperturbative Effects, Non-Commutative Geometry|
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|Deposited By:||Archive Administrator|
|Deposited On:||06 Jan 2006|
|Last Modified:||26 Dec 2012 08:43|
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