One-loop non-planar anomalous dimensions in super Yang-Mills theory

McLoughlin, Tristan; Pereira, Raul; Spiering, Anne

doi:10.1007/jhep10(2020)124

Cited by 8 publications

(10 citation statements)

References 77 publications

(129 reference statements)

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“…See also recent interesting work on non-planar anomalous dimensions[24] 2. The full solution to the spectral problem was obtained by Quantum Spectral Curve[38,39] 3.…”

mentioning

confidence: 99%

Three-point functions in ABJM and Bethe Ansatz

Yang

Jiang

Komatsu

et al. 2022

J. High Energ. Phys.

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We develop an integrability-based framework to compute structure constants of two sub-determinant operators and a single-trace non-BPS operator in ABJM theory in the planar limit. In this first paper, we study them at weak coupling using a relation to an integrable spin chain. We first develop a nested Bethe ansatz for an alternating SU(4) spin chain that describes single-trace operators made out of scalar fields. We then apply it to the computation of the structure constants and show that they are given by overlaps between a Bethe eigenstate and a matrix product state. We conjecture that the determinant operator corresponds to an integrable matrix product state and present a closed-form expression for the overlap, which resembles the so-called Gaudin determinant. We also provide evidence for the integrability of general sub-determinant operators. The techniques developed in this paper can be applied to other quantities in ABJM theory including three-point functions of single-trace operators.

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“…See also recent interesting work on non-planar anomalous dimensions[24] 2. The full solution to the spectral problem was obtained by Quantum Spectral Curve[38,39] 3.…”

mentioning

confidence: 99%

Three-point functions in ABJM and Bethe Ansatz

Yang

Jiang

Komatsu

et al. 2022

J. High Energ. Phys.

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“…Now by working with eigenvectors of P, which is also necessary to fully desymmetrise the spectrum, we can choose a basis of states such that P = +1 and the Hamiltonian is real and symmetric when restricted to these sectors. This construction can be generalised to a time-reversal symmetry of the one-loop non-planar dilatation operator of N = 4 SYM theory by interpreting P as the operator which reverses the order of fields within individual traces of gauge-invariant operators and so explains the GOE statistics seen in [48,49].…”

Section: Level-spacing Statisticsmentioning

confidence: 99%

“…In particular, the BGS conjecture [47] states that quantum-chaotic systems have spectra whose fluctuations are described by Random Matrix Theory (RMT). An analysis of the spectrum of the planar dilatation operator of N = 4 SU(N ) SYM theory expanded in the 't Hooft coupling λ was performed in [48] and [49], and it was shown that, for rank-one sectors of the one-loop planar theory, the spacing between adjacent levels is described by the Poisson distribution as is characteristic of integrable systems [50]. However, when non-planar corrections are included, the spectrum becomes chaotic and the level spacings closely follow the Wigner-Dyson distribution for the Gaussian Orthogonal Ensemble (GOE).…”

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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“…The Bethe states from algebraic Bethe ansatz and the ones from coordinate Bethe ansatz are related by |u, v, w al ∝ i<j u i − u j + i u i − u j i<j v i − v j + i v i − v j i<j w i − w j + i w i − w j |u, v, w co , (D. 24) with a proportional factor which is invariant under the permutations of rapidities of the same type.…”

Section: Nested Algebraic Bethe Ansatzmentioning

confidence: 99%

“…See also recent interesting work on non-planar anomalous dimensions[24] 2. We should however note that the (non-)integrability of the sub-determinant operators is not fully settled even for N = 4 SYM.…”

mentioning

confidence: 98%

Three-Point Functions in ABJM and Bethe Ansatz

Yang,

Jiang,

Komatsu

et al. 2021

Preprint

View full text Add to dashboard Cite

We develop an integrability-based framework to compute structure constants of two subdeterminant operators and a single-trace non-BPS operator in ABJM theory in the planar limit. In this first paper, we study them at weak coupling using a relation to an integrable spin chain. We first develop a nested Bethe ansatz for an alternating SU(4) spin chain that describes single-trace operators made out of scalar fields. We then apply it to the computation of the structure constants and show that they are given by overlaps between a Bethe eigenstate and a matrix product state. We conjecture that the determinant operator corresponds to an integrable matrix product state and present a closed-form expression for the overlap, which resembles the so-called Gaudin determinant. We also provide evidence for the integrability of general sub-determinant operators. The techniques developed in this paper can be applied to other quantities in ABJM theory including three-point functions of single-trace operators.

show abstract

One-loop non-planar anomalous dimensions in super Yang-Mills theory

Cited by 8 publications

References 77 publications

Three-point functions in ABJM and Bethe Ansatz

Three-point functions in ABJM and Bethe Ansatz

Chaotic spin chains in AdS/CFT

Three-Point Functions in ABJM and Bethe Ansatz

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