Holographic Schwinger-Keldysh effective field theories

Heller, Michał; Pinzani-Fokeeva, Natalia

doi:10.1007/jhep05(2019)188

Cited by 62 publications

(86 citation statements)

References 100 publications

(227 reference statements)

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“…The applicability of our effective theory framework to the scenario where the bath is chaotic and strongly coupled implies that it may be possible to construct a holographic dual description [61][62][63][64][65][66][67][68][69] of the particle's non-linear dynamics. The OTO extension of this nonlinear dynamics may be useful in determining a holographic prescription for computing the particle's OTOCs [67,70].…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Out of time ordered effective dynamics of a quartic oscillator

Chakrabarty

Chaudhuri

2019

SciPost Phys.

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We study the dynamics of a quantum Brownian particle weakly coupled to a thermal bath. Working in the Schwinger-Keldysh formalism, we develop an effective action of the particle up to quartic terms. We demonstrate that this quartic effective theory is dual to a stochastic dynamics governed by a non-linear Langevin equation. The Schwinger-Keldysh effective theory, or the equivalent non-linear Langevin dynamics, is insufficient to determine the out of time order correlators (OTOCs) of the particle. To overcome this limitation, we construct an extended effective action in a generalised Schwinger-Keldysh framework. We determine the additional quartic couplings in this OTO effective action and show their dependence on the bath's 4-point OTOCs. We analyse the constraints imposed on the OTO effective theory by microscopic reversibility and thermality of the bath. We show that these constraints lead to a generalised fluctuation-dissipation relation between the non-Gaussianity in the distribution of the thermal noise experienced by the particle and the thermal jitter in its damping coefficient. The quartic effective theory developed in this work provides extension of several results previously obtained for the cubic OTO dynamics of a Brownian particle. Contents SciPost PhysicsSubmission [22,[27][28][29]. Nevertheless, it is interesting to explore the corrections to this effective dynamics by including the cubic and higher degree terms in the analysis. A simple way to obtain such corrections is to extend the Caldeira-Leggett model by introducing a non-linear combination of the bath oscillators' positions in the operator that couples to the particle [29,30].One such extension was discussed in [30] where the oscillators in the bath were divided into two sets (labelled by X and Y). Then apart from the bilinear interactions (which are present in the Caldeira-Leggett model), small cubic interactions were introduced between the particle (q) and pairs of bath oscillators. Each such pair consisted of one oscillator drawn from the set X and the other from the set Y. Due to these cubic interactions, this model was called the 'qXY model'.Introduction of these cubic interactions leads to cubic and higher degree terms in the effective action of the particle. In [30], this effective theory was studied up to the cubic terms in a Markovian limit. It was shown to be dual to a non-linear Langevin dynamics which has perturbative corrections over the linear Langevin dynamics in the Caldeira-Leggett model. The additional parameters in this non-linear dynamics receive contributions from the 3-point correlators of the bath. These 3-point correlators lead to an anharmonicity in the particle's dynamics and a non-Gaussianity in the distribution of the thermal noise experienced by the particle. In addition, they also give rise to thermal jitters 1 in both the frequency and the damping of the particle. The thermal jitter in the damping coefficient and the non-Gaussianity in the noise are connected by a generalised fluctuation-dissipation relation [30...

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Section: Conclusion and Discussionmentioning

confidence: 99%

Out of time ordered effective dynamics of a quartic oscillator

Chakrabarty

Chaudhuri

2019

SciPost Phys.

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“…rephrase our discussion in terms of the more general real-time holography prescriptions of [6][7][8][9][10]45]. In addition to potentially giving us a clearer perspective on the origin of pole-skipping, this formulation would also be the starting point for a generalisation to higher-order correlation functions.…”

Section: Further Constraints From Near-horizon Perturbationsmentioning

confidence: 99%

Horizon constraints on holographic Green’s functions

2020

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We explore a new class of general properties of thermal holographic Green's functions that can be deduced from the near-horizon behaviour of classical perturbations in asymptotically anti-de Sitter spacetimes. We show that at negative imaginary Matsubara frequencies and appropriate complex values of the wavenumber the retarded Green's functions of generic operators are not uniquely defined, due to the lack of a unique ingoing solution for the bulk perturbations. From a boundary perspective these 'pole-skipping' points correspond to locations in the complex frequency and momentum planes at which a line of poles of the retarded Green's function intersects with a line of zeroes. As a consequence the dispersion relations of collective modes in the boundary theory at energy scales ω ∼ T are directly constrained by the bulk dynamics near the black-brane horizon. For the case of conserved U (1) current and energy-momentum tensor operators we give examples where the dispersion relations of hydrodynamic modes pass through a succession of pole-skipping points as real wavenumber is increased. We discuss implications of our results for transport, hydrodynamics and quantum chaos in holographic systems. arXiv:1904.12883v3 [hep-th] 13 Jan 2020 45 E.3 Transverse metric perturbations 48 E.4 Longitudinal metric perturbations 49 E.5 Transverse metric perturbations in a charged black hole 52 -1 -1 v B is the 'butterfly velocity' [15][16][17] of the dual quantum field theory. 2 Pole-skipping in G R εε at (ω * , k * ) was also shown to hold in holographic theories dual to higher derivative gravity in [20].3 The symbol ω n is more conventionally used to refer to the real set of Matsubara frequencies ω E = 2πT n at which the Euclidean Green's function is defined. Here we are interested in studying the real time correlator G R (ω, k) and will abuse the more common notation somewhat by using the symbol ω n to refer to the special pure imaginary frequencies ω = ω n = −i2πT n. These are referred to as the 'negative imaginary Matsubara frequencies' for obvious reasons.We are grateful to Nejc Ceplak, Saso Grozdanov, Hong Liu, and Andrei Starinets for helpful discussions. M. B. received support from the Office of High Energy Physics of U.S.

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“…Physically, the question essentially becomes one of coming up with a prescription ensuring that effects of the outgoing Hawking quanta are correctly accounted for (see [22,23] for attempts in this direction). While a complete answer to this question is still unclear, an interesting prescription was recently given by [31] to address this lacunae in the probe limit (see also [32]).…”

Section: Jhep07(2020)242mentioning

confidence: 99%

“…The authors of[31,32] also addressed the problem of Maxwell gauge field in the probe limit. However, as pointed out in[31] many aspects of how the prescription works for gauge theories are still unclear.3 The non-Gaussian correlations we compute holographically using the semiclassical gravity approximation are suppressed in the planar expansion by powers of 1/N , as indeed are all higher point functions in a large N (or large central charge) environment.…”

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confidence: 99%

Open quantum systems and Schwinger-Keldysh holograms

Jana

Loganayagam

Rangamani

2020

J. High Energ. Phys.

171

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We initiate the study of open quantum field theories using holographic methods. Specifically, we consider a quantum field theory (the system) coupled to a holographic field theory at finite temperature (the environment). We investigate the effects of integrating out the holographic environment with an aim of obtaining an effective dynamics for the resulting open quantum field theory. The influence functionals which enter this open effective action are determined by the real-time (Schwinger-Keldysh) correlation functions of the holographic thermal environment. To evaluate the latter, we exploit recent developments, wherein the semiclassical gravitational Schwinger-Keldysh saddle geometries were identified as complexified black hole spacetimes. We compute real-time correlation functions using holographic methods in these geometries, and argue that they lead to a sensible open effective quantum dynamics for the system in question, a question that hitherto had been left unanswered. In addition to shedding light on open quantum systems coupled to strongly correlated thermal environments, our results also provide a principled computation of Schwinger-Keldysh observables in gravity and holography. In particular, these influence functionals we compute capture both the dissipative physics of black hole quasinormal modes, as well as that of the fluctuations encoded in outgoing Hawking quanta, and interactions between them. We obtain results for these observables at leading order in a low frequency and momentum expansion in general dimensions, in addition to determining explicit results for two dimensional holographic CFT environments.

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Holographic Schwinger-Keldysh effective field theories

Cited by 62 publications

References 100 publications

Out of time ordered effective dynamics of a quartic oscillator

Out of time ordered effective dynamics of a quartic oscillator

Horizon constraints on holographic Green’s functions

Open quantum systems and Schwinger-Keldysh holograms

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