Inheritance principle and non-renormalization theorems at finite temperature

We 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 S3). 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 N=4 super-Yang-Mills theory on S3 survive at finite temperature despite the fact that the conformal and supersymmetries are both broken.