Low-energy dynamics in N = 2 super QED: Two-loop approximation

TL;DR

This paper calculates the two-loop effective action in N=2 supersymmetric QED, revealing a non-zero F^4 correction that challenges previous assumptions about quantum corrections in such theories.

Contribution

It provides an exact evaluation of the two-loop effective action in N=2 SQED and clarifies the presence of F^4 corrections, addressing discrepancies in prior theoretical results.

Findings

Exact two-loop effective action expressed as series in supersymmetric F^{2n} terms

Demonstration of a non-vanishing F^4 quantum correction at two loops

Re-derivation of the F^4 term confirming its existence in N=2 SQED

Abstract

The two-loop (Euler-Heisenberg-type) effective action for N = 2 supersymmetric QED is computed using the N = 1 superspace formulation. The effective action is expressed as a series in supersymmetric extensions of F^{2n}, where n=2,3,..., with F the field strength. The corresponding coefficients are given by triple proper-time integrals which are evaluated exactly. As a by-product, we demonstrate the appearance of a non-vanishing F^4 quantum correction at the two-loop order. The latter result is in conflict with the conclusion of hep-th/9710142 that no such quantum corrections are generated at two loops in generic N = 2 SYM theories on the Coulomb branch. We explain a subtle loophole in the relevant consideration of hep-th/9710142 and re-derive the F^4 term from harmonic supergraphs.