Scrambling in Yang-Mills

Koch, Robert de Mello; Gandote, Eunice; Mahu, Augustine Larweh

doi:10.1007/jhep01(2021)058

Cited by 12 publications

(7 citation statements)

References 116 publications

(202 reference statements)

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“…Developing this idea further is beyond the scope of the present paper. The eventual goal of such a program would be to simplify the types of analysis found in the works [68,69]. It is likely that this basis is close to the so called Gauss graph basis described in [70,71].…”

Section: More Open Stringsmentioning

confidence: 99%

BPS coherent states and localization

Berenstein,

Wang

2022

Preprint

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We introduce coherent states averaged over a gauge group action to study correlators of half BPS states in N = 4 SYM theory. The overlaps of these averaged coherent states are a generating function of correlators and can be written in terms of the Harish-Chandra-Itzykzon-Zuber (HCIZ) integral. We show that this formula immediately leads to a computation of the normalization of two point functions in terms of characters obtained originally in the work of Corley, Jevicki and Ramgoolam. We also find various generalizations for A n−1 quivers that follow directly from other solvable integrals over unitary groups. All of these can be computed using localization methods. When we promote the parameters of the generating function to collective coordinates, there is a dominant saddle that controls the effective action of these coherent states in the regime where they describe single AdS giant gravitons. We also discuss how to add open strings to this formulation. These will produce calculations that rely on correlators of matrix components of unitaries in the ensemble that is determined by the HCIZ integral to determine anomalous dimensions. We also discuss how sphere giants arise from Grassman integrals, how one gets a dominant saddle and how open strings are added in that case. The fact that there is a dominant saddle helps to understand how a 1/N expansion arises for open strings. We generalize the coherent state idea to study 1/4 and 1/8 BPS states as more general integrals over unitary groups.

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Section: More Open Stringsmentioning

confidence: 99%

BPS coherent states and localization

Berenstein,

Wang

2022

Preprint

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“…Our methods and discussions are also related to fuzzball proposal [88]- [93]. There are also scrambling behaviors in heavy and excited states in the gauge theory duals [94,95]. On the other hand, scrambling behaviors have also been observed in fuzzball geometries [93].…”

Section: Discussionmentioning

confidence: 86%

Entanglement and mixed states of Young tableau states in gauge/gravity correspondence

Lin,

Zhu

2021

Preprint

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We use entangled multimode coherent states to produce entangled giant graviton states, in the context of gauge/gravity duality. We make a smeared distribution of the entangled multimode coherent states on the circle, or on the five-sphere, in the higher dimensional view. In gauge/gravity duality, we analyze the superposition of giant graviton states, and the entangled pairs of giant graviton states. We map a class of angular distribution functions to unitary operations on the pairs. We also use Young tableau states to construct cat states and qudit states. Various bipartite quantum states involving Young tableau states are analyzed, including micro-macro entangled states. Mixed states of Young tableau states are generated, by using ensemble mixing using angular distribution functions, and also by going through noisy quantum channels. We then produce mixed entangled pair of giant graviton states, by including interaction with the environment and using noisy quantum channels.

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“…Additional analysis of spectral observables and multi-trace eigenstates provided further evidence that, at finite values of N , the theory is described by GOE RMT. For operators whose dimensions scale as N 2 , and so are sensitive to non-planar effects, the theory has also been shown to exhibit fast scrambling [51].…”

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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Scrambling in Yang-Mills

Cited by 12 publications

References 116 publications

BPS coherent states and localization

BPS coherent states and localization

Entanglement and mixed states of Young tableau states in gauge/gravity correspondence

Chaotic spin chains in AdS/CFT

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