Superconformal $ \mathcal{N} = {3} $ SYM low-energy effective action

Abstract

We construct a manifestly N = 3 supersymmetric low-energy effective action of N = 3 super Yang-Mills theory. The effective action is written in the N = 3 harmonic superspace and respects the full N = 3 superconformal symmetry. On mass shell this action is responsible for the four-derivative terms in the N = 4 SYM effective action, such as F 4 /X 4 and its supersymmetric completions, while off shell it involves also higherderivative terms. For constant Maxwell and scalar fields its bosonic part coincides, up to the F 6 /X 8 order, with the bosonic part of the D3 brane action in the AdS 5 × S 5 background. We also argue that in the sector of scalar fields it involves the correctly normalized Wess-Zumino term with the implicit SU(3) symmetry.

N = 3 $$ \mathcal{N}=3 $$ four dimensional field theories

“…Perhaps other N = 3 theories, beyond the ones discussed here, can be constructed starting from N = 4 theories with other gauge groups. The harmonic superspace formulation of N = 3 SYM may be helpful in this regard [28][29][30][31][32][33][34].…”

Low-energy effective action in 5D,N=2 supersymmetric gauge theory

“…The most prominent example is supplied by the four-derivative term in the low-energy 4D, N = 4 SYM effective action which, in the sector of N = 2 gauge multiplet, is accommodated by a non-holomorphic superfield potential [1]. An N = 4 supersymmetric completion of this potential was constructed in N = 2 harmonic superspace [2,3,4,5], in N = 3 harmonic superspace [6] and in various on-shell N = 4 harmonic superspaces [7,8] (see [9] for a review). By these works, the origin of nonrenormalizability of the N = 4 SYM low-energy effective action against higher-loop quantum corrections was revealed and links with the leading terms in the effective action of D3 brane on the AdS 5 × S 5 background were established.…”

Low-energy effective action in two-dimensional SQED: a two-loop analysis

“…We speculate that these subgroups may be made manifest in other superfield descriptions of the N = (4, 4) gauge theory such as the harmonic superspace [50,51,52,53,54]. Recall that in the 4d N = 4 SYM theory the careful account of all maximal subgroups of the SU(4) R-symmetry group resulted in different but equivalent superfield descriptions of the low-energy effective action [47,48,49,55]. It is tempting to develop similar ideas for the low-energy effective action in 2d supersymmetric gauge theories.…”