• CFT
• conformal
• finite temperature
• high temperature
• O(N)
• twisted partition function

The present thesis will discuss Conformal Field Theories at Finite Temperature.
We will begin by reviewing the basics of conformal geometry, with particular emphasis on studying the conformal algebra of $\mathbb{R}^{p,q}$. We then proceed to review simple aspects of conformal field theories in $\mathbb{R}^{p,q}$, such as $n$-point functions, OPE, and unitarity bounds. After that, we dive into a discussion of various topics about Conformal Field Theories at finite temperature, such as group-theoretical methods and asymptotic expressions for the twisted partition function at high temperature. Finally, we proceed to perform an explicit computation of a twisted partition function for the $O(N)$ $\phi^4$ model on $S^2$, to compare our result to the asymptotic results dictated by the general theory.