A Non-Renormalization Theorem at Finite Temperature

In this thesis we prove a non-renormalization theorem for the 3-points functions of chiral, scalar superconformal primaries in the four-dimensional N=4 SYM at finite temperature. The theorem relies on a known, analogous proof done at zero temperature. In this work we adapt the proof to a finite temperature scenario; in particular, we discuss how to recover the conformal invariance and how to get rid of a soft, thermal breaking term appearing in the superconformal Ward identity, the principal tool exploited in the theorem.