Replica geometries, as a technique emerged recent years in the study of the black hole information paradox, provide an interpretation of the phase transition of the black hole entropy. Recently, Associate Professor Jun Nian and former postdoctoral researcher Yuan Zhong of the International Centre for Theoretical Physics Asia-Pacific (ICTP-AP) at the University of Chinese Academy of Sciences published a paper in the journal Physical Review D investigating the phase structure induced by the connectivity of replica geometries in the low-dimensional effective theory describing the near-horizon fluctuations of near-extremal Reissner-Nordström black holes.
 

   The replica wormhole explanation of black hole entropy phase transitions typically relies on the manual introduction of external entangled systems, such as heat baths or end-of-world branes. This work, by studying the dependence of the entropy of the boundary effective field theory on the coupling constants and the temperature, reveals an intrinsic and rich phase structure of this system. The near-horizon quantum fluctuations of near-extremal RN black holes are described by two-dimensional AdS Jackiw-Teitelboim (JT) gravity coupled to a Maxwell field. This two-dimensional gravity is holographically dual to a one-dimensional field theory described by a Schwarzian mode coupled to a phase mode. The entropy of the one-dimensional field theory system can be computed by the replica trick, which is holographically dual to the replica geometry partition function of the two-dimensional gravity system. By computing the partition functions of the replica geometry in both connected and disconnected configurations, one can determine the phase transition condition. When the entropies contributed by the connected and disconnected geometries cross over each other, a phase transition occurs in the corresponding one-dimensional field theory system.
 
       Within this framework, the team computed the dependence of the entropy on the coupling constants and the temperature, and presented the phase structure in the low-temperature limit. This phase structure depends on both the temperature and three coupling constants of the one-dimensional field theory system. The study also examined the effects of quantum corrections of the Schwarzian mode, and found that in different parameter regimes, the phase transition can be either suppressed or shifted. These results provide a new intrinsic perspective on the phase transition behavior in low-dimensional quantum gravity.
 

       This work was supported by the National Natural Science Foundation of China (Grants No. 12375067 and No. 12547104).
 

       Article link:
 https://doi.org/10.1103/s5vj-rk9g