Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 9, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP09(2022)240
Keywords
AdS-CFT Correspondence; Integrable Field Theories; Supersymmetric Gauge Theory
Categories
Funding
- Science Foundation Ireland
- Science Foundation Ireland [15/CDA/3472]
- ERC [757978]
- Villum Fonden [00025445]
- European Union [764850]
- Science Foundation Ireland (SFI) [15/CDA/3472] Funding Source: Science Foundation Ireland (SFI)
- European Research Council (ERC) [757978] Funding Source: European Research Council (ERC)
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This study investigates the spectrum of anomalous dimensions in planar N = 4 supersymmetric Yang-Mills theory and its deformations. It reveals that a specific deformation of the integrable N = 4 dilatation operator exhibits Wigner-Dyson level statistics at finite coupling but has slower cross-over to chaotic dynamics. For other deformations, it shows strong chaotic dynamics with a spectrum well described by random matrix theory.
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-beta 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-angular-momentum 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-beta SU(3) theory, the resulting Landau-Lifshitz model has classically chaotic dynamics at finite values of the deformation parameter.
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