Chaotic spin chains in AdS/CFT
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Chaotic spin chains in AdS/CFT. / McLoughlin, Tristan; Spiering, Anne.
I: Journal of High Energy Physics, Bind 2022, Nr. 9, 240, 29.09.2022.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Chaotic spin chains in AdS/CFT
AU - McLoughlin, Tristan
AU - Spiering, Anne
PY - 2022/9/29
Y1 - 2022/9/29
N2 - 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.
AB - 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.
KW - AdS-CFT Correspondence
KW - Integrable Field Theories
KW - Supersymmetric Gauge Theory
KW - DILATATION OPERATOR
KW - INTEGRABILITY
KW - STRINGS
KW - DEFORMATIONS
KW - DUALITY
KW - STATES
KW - SYM
U2 - 10.1007/JHEP09(2022)240
DO - 10.1007/JHEP09(2022)240
M3 - Journal article
VL - 2022
JO - Journal of High Energy Physics (Online)
JF - Journal of High Energy Physics (Online)
SN - 1126-6708
IS - 9
M1 - 240
ER -
ID: 322567631