Black Hole in ADS and Quantum Field Theory

TL;DR

This paper reviews recent progress in understanding the thermodynamic and statistical properties of black holes in Anti-de Sitter space through the lens of dual conformal field theories, emphasizing the role of symmetries at critical points.

Contribution

It highlights the connection between quantum field theory symmetries at critical points and black hole thermodynamics within the AdS/CFT correspondence.

Findings

Symmetries of CFT at critical points underpin black hole thermodynamics.

Euclidean CFT time encodes black hole statistical properties.

Recent advances clarify the duality between AdS black holes and boundary field theories.

Abstract

I will present a short review of recent achievements in understanding the origin of the statistical properties versus the thermodynamical ones for Anti De Sitter space--time, ADS$_{n+1}$ from the point of view of the "dual" field theory defined on the boundary of ADS$_{{n+1}}$ conformal invariant, CFT$_n$. We try to convince the audience that the symmetries of Quantum Field Theory at the critical points are, on one side, at the basis of the thermodynamical properties of Black Hole solution, i.e. the Hawking temperature $T_H$ and the entropy $S_H$; on the other side the CFT$_n$ in Euclidean time determines the statistical properties of BH.