Stringy sums and corrections to the quantum string Bethe ansatz

Abstract

We analyze the effects of zeta-function regularization on the evaluation of quantum corrections to spinning strings. Previously, this method was applied in the sl(2) subsector and yielded agreement to third order in perturbation theory with the quantum string Bethe ansatz. In this note we discuss related sums and compare zeta-function regularization against exact evaluation of the sums, thereby showing that the zeta-function regularized expression misses out perturbative as well as non-perturbative terms. In particular, this may imply corrections to the proposed quantum string Bethe equations. This also explains the previously observed discrepancy between the semi-classical string and the quantum string Bethe ansatz in the regime of large winding number.

20 pages; v2: refs and section on exponential corrections added

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• The Zamolodchikov-Faddeev Algebra for AdS_5 x S^5 Superstring
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• Quantum spinning strings in AdS_4 x CP^3: testing the Bethe Ansatz proposal
• Green-Schwarz Strings in TsT-transformed backgrounds
• The AdS5xS5 Superstring in Light-Cone Gauge and its Bethe Equations
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• Infinite spin limit of semiclassical string states
• Integrability and Transcendentality
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• Exact expressions for quantum corrections to spinning strings
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• The magnon kinematics of the AdS/CFT correspondence
• Quantum Wrapped Giant Magnon
• Structure of large spin expansion of anomalous dimensions at strong coupling
• Long-Range GL(n) Integrable Spin Chains and Plane-Wave Matrix Theory
• Classical r-matrix of the su(2|2) SYM spin-chain
• 1/J corrections to semiclassical AdS/CFT states from quantum Landau-Lifshitz model
• Asymptotic Bethe Ansatz from String Sigma Model on S^3 x R
• Double Scaling and Finite Size Corrections in sl(2) Spin Chain
• A Yangian Double for the AdS/CFT Classical r-matrix
• Integrable twists in AdS/CFT
• Reduced sigma-model on AdS_5 x S^5: one-loop scattering amplitudes
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• Higher Loop Bethe Ansatz for Open Spin-Chains in AdS/CFT
• Luescher formula for GKP string
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• Factorized world-sheet scattering in near-flat AdS_5 x S^5
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• Review of AdS/CFT Integrability, Chapter II.2: Quantum Strings in AdS5xS5
• Toy models for wrapping effects
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• Bethe Ansatz solutions for highest states in $\mathcal{N}=4$ SYM and AdS/CFT duality
• Semiclassical Strings in Electric and Magnetic Fields Deformed $Ad{S}_5\times S^5$ Spacetimes
• On string integrability. A journey through the two-dimensional hidden symmetries in the AdS/CFT dualities
• Strong coupling anomalous dimensions of $\mathcal{N}=4$ super Yang-Mills
• Quantum Landau-Lifshitz model at four loops: 1/J and 1/J^2 corrections to BMN energies
• Matrix Models, Complex Geometry and Integrable Systems. II
• Large-Spin Expansions of GKP Strings
• Superspace methods for the computation of wrapping effects in the standard and beta-deformed N=4 SYM
• On type 0 string theory in solvable RR backgrounds
• Highest states in light-cone $Ad{S}_5\times S^5$ superstring
• Wrapping effects in supersymmetric gauge theories
• Generalised scaling at subleading order
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• The SU(1|2) and SU(2|2) Sectors from Superstrings in AdS5 x S5