document: It has recently been demonstrated [15] (see also [13] and references therein) that for a self-dual background the two-loop QED effective action takes a remarkably simple form that is very similar to the one-loop action in the same background. There are expectations that this similarity persists at higher loops, and therefore there should be some remarkable structure encoded in the all-loop effective action for gauge theories. In the supersymmetric case, one has to replace the requirement of self-duality by that of relaxed super self-duality [16] in order to arrive at conclusions similar to those given in [15]. Further progress in this direction may be achieved through the analysis of N=2 covariant supergraphs. Finally, we believe that the results of this Letter may be helpful in the context of the conjectured correspondence [17–19] between the D3-brane action in AdS5×S5 and the low-energy action for N=4 SU(N) SYM on its Coulomb branch, with the gauge group SU(N) spontaneously broken to SU(N−1)×U(1). There have appeared two independent F6 tests of this conjecture [19,20], with conflicting conclusions. The approach advocated here provides the opportunity for a further test.
extractive_keyphrases: ads5×s5 coulomb branch covariant supergraphs f6 tests of this conjecture gauge group higher loops
abstractive_keyphrases: all-loop effective action analysis of n=2 covariant supergraphs d3-brane action one-loop action su(n) su(n−1)×u(1) su(n) sym two-loop qed two-loop qed effective action