Modified "complexity equals action" conjecture

Jiang, Jie; Li, Xiao-Wei

doi:10.48550/arxiv.1903.05476

Cited by 7 publications

(7 citation statements)

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“…In the AdS/CFT correspondence, there are two popular proposals for complexity, usually dubbed by "Complexity=Volume" (CV) duality [7,8] and "Complex-ity=Action" (CA) duality [9,10]. The two conjectures have been extensively studied in literature [11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46]. However, there are some drawbacks for the two proposals as well.…”

Section: Introductionmentioning

confidence: 99%

Time dependence of complexity for Lovelock black holes

Fan

Liang

2019

Phys. Rev. D

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We study the general time dependence of complexity for holographic states dual to Lovelock black holes using the "Complexity=Action" (CA) proposal. We observe that at early times, the critical time at which the complexity begins to increase is a decreasing function of the higher order coupling constants, which implies that the complexity evolves faster than that of Schwarzschild black holes. At late times, the rate of change of complexity is essentially determined by the generalised Gibbons-Hawking-York boundary term evaluated at the future singularity. In particular, its ratio to black hole mass is a characteristic constant, independent of the higher order couplings. Thus, in the vanishing coupling limit, the result in general does not reduce to that of Schwarzschild black holes, in spite of that the metric reduces to the latter as well as the gravitational action. In fact, the two differ by a constant during the whole time evolution. Including the next-to-leading order term around late times, we find that as the Einstein case, the late time limit is always approached from above, thus violating any conjectured upper bound given by the late time result. For charged Lovelock black holes, we find that with sufficient charge, the complexity roughly behaves the same as the Einstein case. However, for smaller charges, the two have some significant differences. In particular, unlike the Einstein case, in the uncharged limit the complexity growth rate does not match with the neutral case, differing by a constant in the whole time evolution.

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Section: Introductionmentioning

confidence: 99%

Time dependence of complexity for Lovelock black holes

Fan

Liang

2019

Phys. Rev. D

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“…There are two proposals put forward by Susskind and his collaborators to quantify the size of the ERB: one is the "complexity=volume"(CV) conjecture [4] which states that the holographic complexity is given by the volume of the codimension-1 maximal spacelike surface in the bulk connecting the left and right sides; the other is the "complex-ity=action"(CA) conjecture [6,7] which states that the holographic complexity is captured by the gravitational action of the bulk region known as the Wheeler-de Witt (WdW) patch bounded by light sheets. Both conjectures introduce the gravitational observables which probe the spacetime region deep behind the black hole horizon, and therefore they have been intensely discussed since their birth [8,9,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34]. Nevertheless, the development is hindered by our poor understanding the quantum complexity in the dual field theory.…”

Section: Introductionmentioning

confidence: 99%

Circuit complexity for generalised coherent states in thermal field dynamics

Guo,

Fan,

Jiang

et al. 2020

Preprint

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In this work, we study the circuit complexity for generalized coherent states in thermal systems by adopting the covariance matrix approach. We focus on the coherent thermal (CT) state, which is non-Gaussian and has a nonvanishing one-point function. We find that even though the CT state cannot be fully determined by the symmetric two-point function, the circuit complexity can still be computed in the framework of the covariance matrix formalism by properly enlarging the covariance matrix. Now the group generated by the unitary is the semiproduct of translation and the symplectic group. If the reference state is Gaussian, the optimal geodesic is still be generated by a horizontal generator such that the circuit complexity can be read from the generalized covariance matrix associated to the target state by taking the cost function to be F 2 . For a single harmonic oscillator, we discuss carefully the complexity and its formation in the cases that the reference states are Gaussian and the target space is excited by a single mode or double modes. We show that the study can be extended to the free scalar field theory.

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“…There have been many studies on CV duality and CA duality, such as the divergence structure [17,18], complexity growth rate [19][20][21][22][23][24][25][26], and the generalization beyond Einstein gravity [27][28][29][30][31](see also [32][33][34]), For example, some of us have tried to relate complexity with the phenomena of the accelerating expansion of our universe [35].…”

Section: Introductionmentioning

confidence: 99%

Complexity growth rate, grand potential and partition function

Sun,

2019

Preprint

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We examine the complexity/volume conjecture and further investigate the possible connections between complexity and partition function. The complexity/volume 2.0 states that the complexity growth rate Ċ ∼ P V . In the standard statistics, there is a fundamental relation among P V , the grand potential Ω and the partition function Z. By using this relation, we are able to construct an ansatz between complexity and partition function. The complexity/partition function relation is then utilized to study the complexity of the thermofield double state of extended SYK models for various conditions. The relation between complexity growth rate and black hole phase transition is also discussed.

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Modified "complexity equals action" conjecture

Cited by 7 publications

References 0 publications

Time dependence of complexity for Lovelock black holes

Time dependence of complexity for Lovelock black holes

Circuit complexity for generalised coherent states in thermal field dynamics

Complexity growth rate, grand potential and partition function

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