2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/178084We present a general proof of an ``inheritance principle'' satisfied by a weakly coupled SU(N) gauge theory with adjoint matter on a class of compact manifolds (like $S^3$). In the large $N$ limit, finite temperature correlation functions of gauge invariant single-trace operators in the low temperature phase are related to those at zero temperature by summing over images of each operator in the Euclidean time direction. As a consequence, various non-renormalization theorems of $\NN=4$ Super-Yang-Mills theory on $S^3$ survive at finite temperature despite the fact that the conformal and supersymmetries are both broken.14 pages, uses harvmac v2: reference added, the role of hep-th/0505148 emphasizedHigh Energy Physics - Theorytext