Melnikov’s method in String Theory

Asano, Yasuhito; Kyono, Hideki; Yoshida, Kentaroh

doi:10.1007/jhep09(2016)103

Cited by 10 publications

(8 citation statements)

References 39 publications

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“…Although chaos in string motion has been studied [11][12][13][14][15][16][17][18][19][20][21] in curved geometries, in view of the chaos bound (1), two important issues are left unsolved: First, the motion of the string needs to be near the black hole horizon, and second, the CFT interpretation of the string motion is indispensable. In this paper we address these two issues, by adopting a suspended string in the AdS black hole geometry.…”

Section: Introductionmentioning

confidence: 99%

Chaos of Wilson loop from string motion near black hole horizon

2018

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To find the origin of chaos near black hole horizon in string-theoretic AdS/CFT correspondence, we perform a chaos analysis of a suspended string in AdS black hole backgrounds. It has a definite CFT interpretation: chaos of Wilson loops, or in other words, sensitive time-evolution of a quark antiquark force in thermal gauge theories. Our nonlinear numerical simulation of the suspended Nambu-Goto string shows chaos, which would be absent in pure AdS background. The calculated Lyapunov exponent λ satisfies the universal bound λ ≤ 2πTH for the Hawking temperature TH. We also analyze a toy model of a rectangular string probing the horizon and show that it contains a universal saddle characterized by the surface gravity 2πTH. Our work demonstrates that the black hole horizon is the origin of the chaos, and suggests a close interplay between chaos and quark deconfinement.

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Section: Introductionmentioning

confidence: 99%

Chaos of Wilson loop from string motion near black hole horizon

2018

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“…By computing the power spectrum, Lyapunov characteristic exponents and Poincaré sections, in [10] it was shown that the motion of classical circular strings in the AdS 5 -Schwarzschild background is chaotic. This was subsequently extended to a wide range of backgrounds such as the AdS soliton background [11], AdS 5 ×T 1,1 [12], other AdS 5 × Einstein 5 spaces [13] and p-brane backgrounds [14][15][16], see also . Moreover, the string motion in the gravity dual of β-deformed N = 4 SYM theory was shown to be chaotic for imaginary values of β [39].…”

Section: Introductionmentioning

confidence: 99%

Chaotic spin chains in AdS/CFT

McLoughlin¹,

Spiering²

2022

Preprint

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We consider the spectrum of anomalous dimensions in planar N = 4 supersymmetric Yang-Mills theory and its N = 1 super-conformal Leigh-Strassler deformations. The two-loop truncation of the integrable N = 4 dilatation operator in the SU(2) sector, which is a next-to-nearest-neighbour deformation of the XXX spin chain, is not strictly integrable at finite coupling and we show that it indeed has Wigner-Dyson level statistics. However, we find that it is only weakly chaotic in the sense that the cross-over to chaotic dynamics is slower than for generic chaotic systems.For the Leigh-Strassler deformed theory with generic parameters, we show that the one-loop dilatation operator in the SU(3) sector is chaotic, with a spectrum that is well described by GUE Random Matrix Theory. For the imaginary-β deformation, the statistics are GOE and the transition from the integrable limit is that of a generic system. This provides a weak-coupling analogue of the chaotic dynamics seen for classical strings in the dual background.We further study the spin chains in the semi-classical limit described by generalised Landau-Lifshitz models, which are also known to describe large-angularmomentum string solutions in the dual theory. We show that for the higher-derivative theory following from the two-loop N = 4 SU(2) spin chain, the maximal Lyapunov exponent is close to zero, consistent with the absence of chaotic dynamics. For the imaginary-β SU(3) theory, the resulting Landau-Lifshitz model has classically chaotic dynamics at finite values of the deformation parameter.

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“…So most wellknown in AdS/CFT have nonintegrable string dynamics: AdS-Schwarzschild, AdS-Reissner-Nordstrom, AdS soliton and AdS-Sasaki-Einstein. 4 Other results on (non)integrability can be found in [29][30][31][32]; the list is not exhaustive. Apart from the usual spherical static black holes (neutral and charged), we consider also non-spherical horizons with constant curvature.…”

Section: Introductionmentioning

confidence: 99%

The bound on chaos for closed strings in Anti-de Sitter black hole backgrounds

Čubrović

2019

J. High Energ. Phys.

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We perform a systematic study of the maximum Lyapunov exponent values λ for the motion of classical closed strings in Anti-de Sitter black hole geometries with spherical, planar and hyperbolic horizons. Analytical estimates from the linearized variational equations together with numerical integrations predict the bulk Lyapunov exponent value as λ ≈ 2πT n, where n is the winding number of the string. The celebrated bound on chaos stating that λ ≤ 2πT is thus systematically modified for winding strings in the bulk. Within gauge/string duality, such strings apparently correspond to complicated operators which either do not move on Regge trajectories, or move on subleading trajectories with an unusual slope. Depending on the energy scale, the out-of-time-ordered correlation functions of these operators may still obey the bound 2πT , or they may violate it like the bulk exponent. We do not know exactly why the bound on chaos can be modified but the indication from the gauge/string dual viewpoint is that the correlation functions of the dual gauge operators never factorize and thus the original derivation of the bound on chaos does not apply. arXiv:1904.06295v3 [hep-th] 2 Oct 2019 4 In [25,28] it was shown that Reissner-Nordstrom black holes in asymptotically flat space are also nonintegrable.5 In fact, constant-curvature black holes would be a more suitable term than topological black holes.-4 -

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Melnikov’s method in String Theory

Cited by 10 publications

References 39 publications

Chaos of Wilson loop from string motion near black hole horizon

Chaos of Wilson loop from string motion near black hole horizon

Chaotic spin chains in AdS/CFT

The bound on chaos for closed strings in Anti-de Sitter black hole backgrounds

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