On the two-loop four-derivative quantum corrections in 4D N=2 superconformal field theories

Abstract In N =2,4 superconformal field theories in four space–time dimensions, the quantum corrections with four derivatives are believed to be severely constrained by non-renormalization theorems. The strongest of these is the conjecture formulated by Dine and Seiberg in hep-th/9705057 that such terms are generated only at one loop. In this note, using the background field formulation in N =1 superspace, we test the Dine–Seiberg proposal by comparing the two-loop F 4 quantum corrections in two different superconformal theories with the same gauge group SU ( N ): (i) N =4 SYM (i.e., N =2 SYM with a single adjoint hypermultiplet); (ii) N =2 SYM with 2 N hypermultiplets in the fundamental. According to the Dine–Seiberg conjecture, these theories should yield identical two-loop F 4 contributions from all the supergraphs involving quantum hypermultiplets, since the pure N =2 SYM and ghost sectors are identical provided the same gauge conditions are chosen. We explicitly evaluate the relevant two-loop supergraphs and observe that the F 4 corrections generated have different large N behaviour in the two theories under consideration. Our results are in conflict with the Dine–Seiberg conjecture.