Abstract
We compute the ultraviolet divergences of holographic subregion complexity for the left and right factors of the thermofield double state in warped AdS3 black holes, both for the action and the volume conjectures. Besides the linear divergences, which are also present in the BTZ black hole, additional logarithmic divergences appear. For the action conjecture, these log divergences are not affected by the arbitrarity in the length scale associated with the counterterm needed to ensure reparameterization invariance. We find that the subregion action complexity obeys the superadditivity property for the thermofield double in warped AdS3, independently from the action counterterm coefficient. We study the temperature dependence of subregion complexity at constant angular momentum and we find that it is correlated with the sign of the specific heat.
Highlights
Of quantum gates and of the allowed tolerance in the accuracy with which the final state is prepared
We find that the subregion action complexity obeys the superadditivity property for the thermofield double in warped AdS3, independently from the action counterterm coefficient
The Complexity=Action (CA) [17, 18] refers to a gravitational action IWDW computed in the Wheeler-De Witt (WDW) patch, which is the union of all the spacelike slices that can be attached to the boundary at a given time
Summary
Black holes in asymptotically warped AdS3 spacetime [50, 64, 65] are described by the following metric ds l2. The inner and outer horizons are placed in r−, r+ and ν is a warping parameter such that for ν = 1 the metric gives the BTZ black hole [66, 67]. That the range of variables is: r0 ≤ r < ∞, −∞ < t < ∞ and θ ∼ θ + 2π This metric is pathologic when ν2 < 1, because admits closed timelike curves. Mass and angular momentum depend on the gravitational action we choose, and for our computations we will consider warped BHs arising as a solution of Einstein gravity plus Maxwell and Chern-Simons terms [68, 69]. The conserved charges (mass and angular momentum) are [68, 69]:
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