Complexity and action for warped AdS black holes

Auzzi, Roberto; Baiguera, Stefano; Grassi, M.; Nardelli, Giuseppe; Zenoni, Nicolò

doi:10.1007/jhep09(2018)013

Cited by 45 publications

(26 citation statements)

References 75 publications

(113 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…20, we explore the linear regime and saturation of entanglement evolution on a circle for N = 2001 and β = 0.01L, for masses ranging from mL = 0.001 to 100, where we increase 40 We would like to thank Pasquale Calabrese for pointing this out to us. 41 In fact, we fix the values of the dimensionless parameters m L and β/L. the mass by a factor of 10 in each step.…”

Section: Numerical Resultsmentioning

confidence: 99%

Complexity and entanglement for thermofield double states

et al. 2019

View full text Add to dashboard Cite

Motivated by holographic complexity proposals as novel probes of black hole spacetimes, we explore circuit complexity for thermofield double (TFD) states in free scalar quantum field theories using the Nielsen approach. For TFD states at t = 0, we show that the complexity of formation is proportional to the thermodynamic entropy, in qualitative agreement with holographic complexity proposals. For TFD states at t > 0, we demonstrate that the complexity evolves in time and saturates after a time of the order of the inverse temperature. The latter feature, which is in contrast with the results of holographic proposals, is due to the Gaussian nature of the TFD state of the free bosonic QFT. A novel technical aspect of our work is framing complexity calculations in the language of covariance matrices and the associated symplectic transformations, which provide a natural language for dealing with Gaussian states. Furthermore, for free QFTs in 1+1 dimension, we compare the dynamics of circuit complexity with the time dependence of the entanglement entropy for simple bipartitions of TFDs. We relate our results for the entanglement entropy to previous studies on non-equilibrium entanglement evolution following quenches. We also present a new analytic derivation of a logarithmic contribution due to the zero momentum mode in the limit of vanishing mass for a subsystem containing a single degree of freedom on each side of the TFD and argue why a similar logarithmic growth should be present for larger subsystems. 1 arXiv:1810.05151v4 [hep-th] 15 Feb 2019 C Matrix generators for Sp(4, R) 87 D Comments on bases 88 E Complexity of formation in the diagonal basis 91 F Minimal geodesics for N degrees of freedom with λ R = 1 95 G Derivation of the TFD covariance matrix in terms of matrix functions 105 References 107

show abstract

Section: Numerical Resultsmentioning

confidence: 99%

Complexity and entanglement for thermofield double states

et al. 2019

View full text Add to dashboard Cite

show abstract

“…The first estimates of the late time holographic complexity growth rate for rotating AdS black holes appeared in [7,16], before a complete understanding of how to treat the action contributions of null boundaries was developed in [9]. For lower dimensional black holes, this computation was revisited in [51,52]. They studied the CV and CA growth rate in three dimensional warped AdS black holes, which include rotating BTZ as a subcase.…”

Section: Introductionmentioning

confidence: 99%

Holographic and QFT complexity with angular momentum

Bernamonti

Bigazzi

Billo

et al. 2021

J. High Energ. Phys.

View full text Add to dashboard Cite

We study the influence of angular momentum on quantum complexity for CFT states holographically dual to rotating black holes. Using the holographic complexity=action (CA) and complexity=volume (CV) proposals, we study the full time dependence of complexity and the complexity of formation for two dimensional states dual to rotating BTZ. The obtained results and their dependence on angular momentum turn out to be analogous to those of charged states dual to Reissner-Nordström AdS black holes. For CA, our computation carefully accounts for the counterterm in the gravity action, which was not included in previous analysis in the literature. This affects the complexity early time dependence and its effect becomes negligible close to extremality. In the grand canonical ensemble, the CA and CV complexity of formation are linear in the temperature, and diverge with the same structure in the speed of light angular velocity limit. For CA the inclusion of the counterterm is crucial for both effects. We also address the problem of studying holographic complexity for higher dimensional rotating black holes, focusing on the four dimensional Kerr-AdS case. Carefully taking into account all ingredients, we show that the late time limit of the CA growth rate saturates the expected bound, and find the CV complexity of formation of large black holes diverges in the critical angular velocity limit. Our holographic analysis is complemented by the study of circuit complexity in a two dimensional free scalar model for a thermofield double (TFD) state with angular momentum. We show how this can be given a description in terms of non-rotating TFD states introducing mode-by-mode effective temperatures and times. We comment on the similarities and differences of the holographic and QFT complexity results.

show abstract

“…Then, for the case of warped geometries, the results of path-integral complexity could be compared with those of holographic calculations using the complexity = action or complexity = volume [24][25][26].…”

Section: Building Quantum Circuits From Kac-moody Symmetry Gatesmentioning

confidence: 99%

“…Also, in this setup, it has been shown that the entropy of a thermal state matches with the entropy of a warped BTZ black hole. In addition, the calculations for entanglement entropy and even subregion complexity have already been done for such solutions [24][25][26]. Furthermore, interesting relationships between WCFTs which show semi-local properties and other models such as SYK with complex fermions which has maximal chaos have been found in [27].…”

Section: Introductionmentioning

confidence: 99%