More on complexity of operators in quantum field theory

Yang, Run-Qiu; An, Yuting; Niu, Chao; Zhang, Cheng-Yong; Kim, Keun‐Young

doi:10.1007/jhep03(2019)161

Cited by 44 publications

(50 citation statements)

References 60 publications

(174 reference statements)

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“…However, some progress has been made to ease this predicament. Field theory techniques for defining and calculating complexity where investigated in [13][14][15][16][17][18][19][20][21][22] following the geometric ideas of [1,2], in [23][24][25][26] following path integral methods and in [27,28] following an axiomatic approach. A fascinating connection with group theory was investigated in [29].…”

Section: ∝ V(σ)mentioning

confidence: 99%

WdW-patches in AdS3 and complexity change under conformal transformations II

Flory

2019

J. High Energ. Phys.

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We study the null-boundaries of Wheeler-de Witt (WdW) patches in three dimensional Poincaré-AdS, when the selected boundary timeslice is an arbitrary (nonconstant) function, presenting some useful analytic statements about them. Special attention will be given to the piecewise smooth nature of the null-boundaries, due to the emergence of caustics and null-null joint curves. This is then applied, in the spirit of one of our previous papers, to the problem of how the complexity of the CFT 2 groundstate changes under a small local conformal transformation according to the action (CA) proposal. In stark contrast to the volume (CV) proposal, where this change is only proportional to the second order in the infinitesimal expansion parameter σ, we show that in the CA case we obtain terms of order σ and even σ log(σ). This has strong implications for the possible field-theory duals of the CA proposal, ruling out an entire class of them.2 In contrast to the notations and convention of [40,45], we are using a coordinate z instead of λ, with λ = 1/z 2 .3 We use this term instead of lightsheet, as a priori the lightfronts bounding a WdW-patch do not have to satisfy the necessary requirements to be lightsheets according the the definition of [47].7 See also [62] for related, but more general results.

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Section: ∝ V(σ)mentioning

confidence: 99%

WdW-patches in AdS3 and complexity change under conformal transformations II

Flory

2019

J. High Energ. Phys.

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“…This motivates people to search new proposals for complexity [47,48,49]. In addition, the active research in holography promotes studies of complexity for quantum field theories [50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66] as well as in condensed matter physics [67].…”

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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“…Recently, Nielsen's approach has been adopted in highenergy physics to quantify the complexity of quantum field theory states [6][7][8][9][10][11][12][13][14][15][16][17][18]. This is motivated, in part, by previous conjectures that relate the complexity of the boundary field theory to the bulk space-time geometry, i.e.…”

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confidence: 99%