Inheritance principle and Non-renormalization theorems at finite temperature

We show that in the large N limit, a weakly coupled SU(N) gauge theory with adjoint matter on a class of compact manifolds (like S) satisfies an “inheritance principle” in the low temperature phase. Finite temperature correlation functions of gauge invariant single-trace operators are related to those at zero temperature by summing over images of each operator in the Euclidean time direction. This implies that the corresponding finite temperature string theory dual can be formulated as a sigma model with Euclidean time direction periodically compactified. As a consequence, various non-renormalization theorems of N = 4 Super-Yang-Mills theory survive at finite temperature despite the fact that the conformal and supersymmetries are both broken.