This paper extends the authors' previous work on the holographic interpretation of entanglement entropy in conformal field theories (CFTs) using the AdS/CFT correspondence. It includes several new results and a more detailed review of relevant recent progress. The main contributions are:
1. **Derivation of Entanglement Entropy in AdS$_3$/CFT$_2$**: A more direct derivation of the claim that entanglement entropy is related to minimal area surfaces in AdS$_3$/CFT$_2$ is provided, along with further discussions on higher-dimensional cases.
2. **Entanglement Entropy and Central Charges in 4D CFTs**: The relation between entanglement entropy and central charges in 4D CFTs is examined. The logarithmic part of the 4D entanglement entropy computed in the CFT side is shown to agree with the AdS$_5$ result under specific conditions.
3. **Estimation of Entanglement Entropy in Massive Theories**: The entanglement entropy of massive theories in generic dimensions is estimated using the proposed holographic approach.
The paper also reviews the basic properties of entanglement entropy, including its definition, properties, and its behavior in quantum field theories (QFTs) and conformal field theories (CFTs). It discusses the area law for entanglement entropy in QFTs and the holographic interpretation of entanglement entropy in higher-dimensional CFTs. The authors explore the entanglement entropy of massless free fields and the entropic $c$-function, providing a rough estimation and an exact estimation for the entanglement entropy in 4D gauge theories. Finally, they discuss the connection between entanglement entropy and central charges in 4D CFTs, extending the findings from 2D CFTs.This paper extends the authors' previous work on the holographic interpretation of entanglement entropy in conformal field theories (CFTs) using the AdS/CFT correspondence. It includes several new results and a more detailed review of relevant recent progress. The main contributions are:
1. **Derivation of Entanglement Entropy in AdS$_3$/CFT$_2$**: A more direct derivation of the claim that entanglement entropy is related to minimal area surfaces in AdS$_3$/CFT$_2$ is provided, along with further discussions on higher-dimensional cases.
2. **Entanglement Entropy and Central Charges in 4D CFTs**: The relation between entanglement entropy and central charges in 4D CFTs is examined. The logarithmic part of the 4D entanglement entropy computed in the CFT side is shown to agree with the AdS$_5$ result under specific conditions.
3. **Estimation of Entanglement Entropy in Massive Theories**: The entanglement entropy of massive theories in generic dimensions is estimated using the proposed holographic approach.
The paper also reviews the basic properties of entanglement entropy, including its definition, properties, and its behavior in quantum field theories (QFTs) and conformal field theories (CFTs). It discusses the area law for entanglement entropy in QFTs and the holographic interpretation of entanglement entropy in higher-dimensional CFTs. The authors explore the entanglement entropy of massless free fields and the entropic $c$-function, providing a rough estimation and an exact estimation for the entanglement entropy in 4D gauge theories. Finally, they discuss the connection between entanglement entropy and central charges in 4D CFTs, extending the findings from 2D CFTs.