Deformed gauge theory: Twist versus Seiberg-Witten approach

Abstract

In this chapter we discuss two possible ways of introducing gauge theories on noncommutative spaces. In the first approach the algebra of gauge transformations is unchanged, but the Leibniz rule is changed (compared with gauge theories on commutative space). Consistency of the equations of motion requires enveloping algebravalued gauge fields, which leads to new degrees of freedom. In the second approach we have to go to the enveloping algebra again if we want noncommutative gauge transformations to close in the algebra. However, no new degrees of freedom appear here because of the Seiberg-Witten map. This map enables one to express noncommutative gauge parameters and fields in terms of the corresponding commutative variables. © 2009 Springer.