Less is More: Non-renormalization Theorems from Lower Dimensional Superspace

TL;DR

The paper introduces a lower-dimensional superspace formalism to expose non-renormalization theorems in ${\cal N}=4$ and ${\cal N}=2$ Super-Yang-Mills theories by embedding operators into chiral rings of a reduced SUSY algebra. By formulating ${\cal N}=4$ in ${\cal N}=4$, $d=1$ and ${\cal N}=2$ in ${\cal N}=2$, $d=3$ superspace, it identifies chiral Wilson loops and lines whose expectation values are protected and calculable exactly, leveraging shape invariance and the absence of Konishi anomalies. The results connect to known conjectures (e.g., Zarembo) and extend to higher-dimension cases with appropriate four-supercharge subalgebras, offering exact relations to Higgs-branch operators and clarifying when such non-renormalization results hold. Overall, the work provides a robust, symmetry-based route to exact Wilson-type observables in highly supersymmetric gauge theories and broadens the toolbox for studying non-perturbative features in these models.

Abstract

We discuss a new class of non-renormalization theorems in N=4 and N=2 Super-Yang-Mills theory, obtained by using a superspace which makes a lower dimensional subgroup of the full supersymmetry manifest. Certain Wilson loops (and Wilson lines) belong to the chiral ring of the lower dimensional supersymmetry algebra, and their expectation values can be computed exactly.