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

TL;DR

This paper tests the Dine-Seiberg conjecture on quantum corrections in 4D N=2 superconformal theories by comparing two different models at two loops, finding discrepancies that challenge the conjecture.

Contribution

It provides a direct two-loop comparison of quantum corrections in two superconformal theories, revealing violations of the Dine-Seiberg non-renormalization conjecture.

Findings

Two-loop F^4 corrections differ between the two theories.

Large N behavior of corrections is not identical as predicted.

Results conflict with the Dine-Seiberg conjecture.

Abstract

In \cN = 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 \cN = 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) \cN = 4 SYM (i.e. \cN = 2 SYM with a single adjoint hypermultiplet); (ii) \cN = 2 SYM with 2N 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 \cN = 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.