Comments on the negative specific heat of the TT¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ T\overline{T} $$\end{document} deformed symmetric product CFT

We show that the TT¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ T\overline{T} $$\end{document} deformation of conformal field theories whose entropy grows as S(E) ∼ Eγ for γ > 1/2 exhibits negative specific heat in its microcanonical thermodynamic function S(ℇ). We analyze the large N symmetric product CFT as a concrete example of a CFT with this property and compute the thermodynamic functions such as S(ℇ) and ℇ(T). The negative specific heat in the microcanonical data is interpreted as signaling the first order phase transition when the system is coupled to a heat bath.