Exact islands scenario for CFT systems and critical ratios in higher geometry

TL;DR

This paper investigates entanglement entropy in symmetric CFT systems with a focus on island contributions, revealing critical ratios, exact island scenarios, and entropy identities relevant for higher-dimensional conformal field theories.

Contribution

It introduces an exact island scenario for $CFT_d$ with $d>2$, identifies Fibonacci-type critical ratios for maximum bath entropy, and derives key entropy identities and laws for entanglement.

Findings

Maximum bath entropy occurs at Fibonacci-type ratios.

Beyond critical point, entropy decreases with island effects.

An exact resummation of iceberg contributions leads to the 'exact island' scenario.

Abstract

We study $CFT_d$ systems which are in contact with each other and symmetrically arranged. The system-B is treated as bath that surrounds system-A in the middle. Our focus is to learn how the entanglement entropy of a bath pair system changes as a function of its size. The total size of systems A and B taken together is kept fixed in this process. It is found that for strip shaped systems the bath entropy becomes maximum when respective system sizes follow Fibonacci type critical ratio condition. Beyond critical point when bath size increases the bath entropy starts decreasing, where island and icebergs entropies play important role. Interestingly entire effect of icebergs can be resummed giving rise to 'exact island' scenario for $CFT_d$ with $d>2$. Post criticality we also find important identity involving entropy differences $S[B]-S[A]=S_l-S_{island}$ where island contribution is exact. The mutual information of far separated bath pair follows specific law $I(B:B) \propto {b^2\over (Distance)^d}$. It never vanishes for finite systems. Once system-A size approaches to Kaluza-Klein scale the bath entropy becomes discretized. In summary knowing island corrections is vital for large bath entanglement entropy.