MS Seminar (Mathematics - String Theory)

Speaker: Kanato Goto(University of Tokyo)
Title: Holographic Complexity in the Jackiw-Teitelboim Gravity
Date: Tue, Feb 26, 2019, 13:15 - 14:30
Place: Seminar Room A
Related File: 2263.pdf
Abstract: In the last few years, a deep connection between spacetime geometry and quantum information theoretic properties has been found in the context of AdS/ CFT correspondence. The most famous example is the so-called Ryu-Takayanagi formula which relates the area of the co-dimension two surface in AdS to the entanglement entropy in the CFT. Recently, a new gravity/information connection was found between the size of the interior region of black holes in AdS and the computational complexity in the CFT.
In joint work with Marrochio, Myers, Queimada, and Yoshida, we analyzed the behavior of the holographic complexity in the so-called Jackiw-Teitelboim model (JT model), which is the two-dimensional dilaton gravity theory which describes the nearly AdS2 geometry. In the Complexity=Action proposal, we showed that the late-time growth rate vanishes for the JT model. This vanishing complexity mirrors the behavior for the magnetic Reissner-Nordstrom-AdS black holes in four dimensions, which play a role in constructing the JT action via dimensional reduction. This situation can be ameliorated by instead considering a dimensional reduction describing the near-horizon physics of near-extremal electric black holes in four dimensions. We found that in the resulting two-dimensional dilaton gravity theory, which we call JT-like theory, the late time growth rate is non-vanishing and it approaches the value of the Lloyd bound.
In four dimensions, there is a boundary term involving the Maxwell field, which one can add to the gravitational action. We also considered the dimensional
reduction of the Maxwell boundary term and found that it changes the late time behavior of the complexity for both cases.