Products defined in the context of noncommutative gauge theory allow for an interpolation between exact results on tachyon potentials at zero and large background B-fields. Techniques for computations of effective actions are transposed from the framework
wherethehigher-degreedeformedk-aryoperatorscontribute:
1 1 k= dτ1...dτkexp{iπaij(2τij (τij))}(2sin(πτij))2tij.
001≤i<j≤k
Wesymbolicallydenotetheresultby
Z(T)=dx
k+1
(k+1)!
k!X µ1...X µk µ1... µkFµν(x).