Decoding perturbation theory using resurgence: Stokes phenomena, new saddle points and Lefschetz thimbles

Cherman, Aleksey; Dorigoni, Daniele; Ünsal, Mithat

doi:10.48550/arxiv.1403.1277

Cited by 57 publications

(103 citation statements)

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“…Conclusions -Recent advances in applying the theory of resurgence to quantum theories [25][26][27][28][29][30] have motivated us to rethink the foundational aspects of relativistic hydrodynamics.…”

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confidence: 99%

Hydrodynamics Beyond the Gradient Expansion: Resurgence and Resummation

2015

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Consistent formulations of relativistic viscous hydrodynamics involve short-lived modes, leading to asymptotic rather than convergent gradient expansions. In this Letter we consider the Müller-Israel-Stewart theory applied to a longitudinally expanding quark-gluon plasma system and identify hydrodynamics as a universal attractor without invoking the gradient expansion. We give strong evidence for the existence of this attractor and then show that it can be recovered from the divergent gradient expansion by Borel summation. This requires careful accounting for the short-lived modes which leads to an intricate mathematical structure known from the theory of resurgence.

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confidence: 99%

Hydrodynamics Beyond the Gradient Expansion: Resurgence and Resummation

2015

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“…There is also another type of interpolating functions[8], which is not special case of the FPR. This has been applied to O(N ) non-linear sigma model.2 Note that our interpolating function approach is different from resurgence approach, which has been recently studied in a series of works[9,10,11,12,13,14,15,16,17,18,19,20,21,22,23]. While we use single types of weak and strong coupling expansions as input data, the resurgence approach uses weak coupling expansions around multiple saddle points and does not use strong coupling expansion.…”

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confidence: 99%

Interpolating function and Stokes phenomena

Honda

Jatkar

2015

Nuclear Physics B

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When we have two expansions of physical quantity around two different points in parameter space, we can usually construct a family of functions, which interpolates the both expansions. In this paper we study analytic structures of such interpolating functions and discuss their physical implications. We propose that the analytic structures of the interpolating functions provide information on analytic property and Stokes phenomena of the physical quantity, which we approximate by the interpolating functions. We explicitly check our proposal for partition functions of zero-dimensional ϕ 4 theory and Sine-Gordon model. In the zero dimensional Sine-Gordon model, we compare our result with a recent result from resurgence analysis. We also comment on construction of interpolating function in Borel plane.

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“…Note that (13) has two independent solutions. The solution in (14) was picked on the grounds that there should be only ingoing wave at the horizon, z = 0. (we will elaborate on the boundary conditions in more detail when we discuss the Stokes phenomenon) This solution is to be matched with the far region solution and for this we need the asymptotic expansion of ( 14) for large r (z → 1).…”

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confidence: 99%

“…For this, the identification dominant and subdominant solutions is essential. In quantum mechanical scattering problems, the Stokes phenomenon gives rise to the reflection phenomena [13] and also plays a key role, in somewhat different context, in the application of resurgence theory to the perturbative expansions of quantum field theories [14,15]. As we will discuss shortly, the Hawking quanta responsible for the emission is encoded by the subdominant solution in the horizon region and the appearance of such solution is in fact brought by the requirement of causality.…”

Section: Re Tmentioning

confidence: 99%

Stokes phenomenon and Hawking Radiation

Dumlu

2020

Preprint

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We compute the semiclassical decay rate for Kerr black hole by deriving a one-way connection formula, relating the near horizon solution to the outgoing solution at infinity. In particular, we discuss the relevance of the Stokes phenomenon and show how it leads to a Boltzmann-like thermal weight factor by making use of the Stokes diagrams. We also give the exact result for the semiclassical greybody factor e −2S , where S is the leading order WKB action. We contrast our results with Maldacena and Strominger's work [Phys. Rev. D 56, 4975 (1997)], where the emission spectrum for a rotating black hole was computed locally via asymptotic matching. We find that the relative error of semiclassical decay rate with respect to asymptotic matching formula diminishes in the limit of large angular momentum, l, as expected. In this limit, the action assumes a compact form: 2S ∼ (2l + 1)(Log 16 z0 − 1), where z 0 is the cross ratio formed by the critical points (zeroes) of the scattering potential.

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Decoding perturbation theory using resurgence: Stokes phenomena, new saddle points and Lefschetz thimbles

Cited by 57 publications

References 0 publications

Hydrodynamics Beyond the Gradient Expansion: Resurgence and Resummation

Hydrodynamics Beyond the Gradient Expansion: Resurgence and Resummation

Interpolating function and Stokes phenomena

Stokes phenomenon and Hawking Radiation

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