Bethe Ansatz for Quantum Strings

Abstract

We propose Bethe equations for the diagonalization of the Hamiltonian of quantum strings on AdS_5 x S^5 at large string tension and restricted to certain large charge states from a closed su(2) subsector. The ansatz differs from the recently proposed all-loop gauge theory asymptotic Bethe ansatz by additional factorized scattering terms for the local excitations. We also show that our ansatz quantitatively reproduces everything that is currently known about the string spectrum of these states. Firstly, by construction, we recover the integral Bethe equations describing semiclassical spinning strings. Secondly, we explain how to derive the 1/J energy corrections of arbitrary M-impurity BMN states, provide explicit, general formulae for both distinct and confluent mode numbers, and compare to asymptotic gauge theory. In the special cases M=2,3 we reproduce the results of direct quantization of Callan et al. Lastly, at large string tension and relatively small charge we recover the famous 2 (n^2 lambda)^(1/4) asymptotics of massive string modes at level n. Remarkably, this behavior is entirely determined by the novel scattering terms. This is qualitatively consistent with the conjecture that these terms occur due to wrapping effects in gauge theory. Our finding does not in itself cure the disagreements between gauge and string theory, but leads us to speculate about the structure of an interpolating Bethe ansatz for the AdS/CFT system at finite coupling and charge.

22 pages, LaTeX, JHEP3.cls;v2: minor changes, typos fixed; v3: explicit, general formula for confluent mode numbers obtained

References in corpus (7)

• Semiclassical relativistic strings in S^5 and long coherent operators in N=4 SYM theory
• Large spin limits of AdS/CFT and generalized Landau-Lifshitz equations
• Higher Impurity AdS/CFT Correspondence in the Near-BMN Limit
• Two-loop commuting charges and the string/gauge duality
• Bethe ansatz and fluctuations in SU(3) Yang-Mills operators
• The Circular, Elliptic Three Spin String from the SU(3) Spin Chain
• Pulsating strings in warped AdS_6 x S^4 geometry

Cited by in corpus (442)

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• A Crossing-Symmetric Phase for AdS_5 x S^5 Strings
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• A three-loop test of the dilatation operator in N=4 SYM
• A Generalized Scaling Function for AdS/CFT
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• Complete 1-loop test of AdS/CFT
• Massive S-matrix of AdS_3 x S^3 x T^4 superstring theory with mixed 3-form flux
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• On T-Duality and Integrability for Strings on AdS Backgrounds
• Dressing the Giant Magnon
• The Bethe ansatz approach for factorizable centrally extended S-matrices
• Strong-coupling expansion of cusp anomaly from quantum superstring
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• Stringy sums and corrections to the quantum string Bethe ansatz
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• Quantum strings in AdS_5 x S^5: strong-coupling corrections to dimension of Konishi operator
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• Exploring the mirror TBA
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• Finite-gap equations for strings on AdS_3 x S^3 x T^4 with mixed 3-form flux
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• World-sheet scattering in AdS_5 x S^5 at two loops
• Comment on the Scaling Function in AdS4 x CP3
• (Non)-Integrability of Geodesics in D-brane Backgrounds
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• The Quantum Deformed Mirror TBA I
• Two-dimensional S-matrices from unitarity cuts
• Quantum Wrapped Giant Magnon
• Magnons, Classical Strings and beta-Deformations
• Konishi operator at intermediate coupling
• Simplified TBA equations of the AdS_5 x S^5 mirror model
• The Bound State S-Matrix for AdS5 x S5 Superstring
• Generalized cusp in AdS_4 x CP^3 and more one-loop results from semiclassical strings
• Constructing the AdS/CFT dressing factor
• Two-loop Integrability of Planar N=6 Superconformal Chern-Simons Theory
• Functional BES equation
• Strings as Multi-Particle States of Quantum Sigma-Models
• Embedding nonlinear O(6) sigma model into N=4 super-Yang-Mills theory
• Finite size effects in ferromagnetic spin chains and quantum corrections to classical strings
• Planar plane-wave matrix theory at the four loop order: Integrability without BMN scaling
• The one-loop worldsheet S-matrix for the AdS(n) x S(n) x T(10-2n) superstring
• On Drinfeld's second realization of the AdS/CFT su(2|2) Yangian
• PSU(2,2|4) Character of Quasiclassical AdS/CFT
• N-Impurity Superstring Spectra Near the pp-Wave Limit
• Finite size effects for giant magnons on physical strings
• Large spin corrections in $\mathcal{N}=4$ SYM sl(2): still a linear integral equation
• Y-system for form factors at strong coupling in AdS5 and with multi-operator insertions in AdS3
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• Quantum integrability and functional equations
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• Twisting the Mirror TBA
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• Four-Loop Collinear Anomalous Dimension in N = 4 Yang-Mills Theory
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• Duality between Wilson loops and gluon amplitudes
• On Hidden Symmetries of a Super Gauge Theory and Twistor String Theory
• Towards a string bit formulation of N=4 super Yang-Mills
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• Comments on the Boundary Scattering Phase
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• Open string integrability and AdS/CFT
• Generalized unitarity and the worldsheet S matrix in AdS_n x S^n x M^(10-2n)
• Reflecting Magnon Bound States
• Lectures on S-matrices and Integrability
• The generalised scaling function: a note
• Semiclassical strings in AdS_5 x S^5 and scalar operators in N=4 SYM theory
• Perturbative study of the transfer matrix on the string worldsheet in AdS(5)xS(5)
• Bound State Transfer Matrix for AdS5 x S5 Superstring
• The AdS(n) x S(n) x T(10-2n) BMN string at two loops
• Matching gauge theory and string theory in a decoupling limit of AdS/CFT
• Spin Chain for Quantum Strings
• A two-loop test for the factorised S-matrix of planar N=4
• Asymptotic Bethe Ansatz S-matrix and Landau-Lifshitz type effective 2-d actions
• The SU(2) sector in AdS/CFT
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• From Polygon Wilson Loops to Spin Chains and Back
• The Zamolodchikov-Faddeev algebra for open strings attached to giant gravitons
• Reciprocity of gauge operators in N=4 SYM
• The AdS(4) x CP(3) string and its Bethe equations in the near plane wave limit
• Baxter equation for long-range SL(2|1) magnet
• Landau-Lifshitz sigma-models, fermions and the AdS/CFT correspondence
• On the Scattering of Magnon Boundstates
• Superspace calculation of the three-loop dilatation operator of N=4 SYM theory
• Lattice Super Yang-Mills: A Virial Approach to Operator Dimensions
• Finite-size corrections for quantum strings on AdS_4 x CP^3
• Yangian Symmetry of Long-Range gl(N) Integrable Spin Chains
• Singularities of the Magnon Boundstate S-Matrix
• The ${\mathrm{AdS}}_3\times {\mathrm{S}}^3\times {\mathrm{S}}^3\times {\mathrm{S}}^1$ worldsheet S matrix
• Slow-string limit and "antiferromagnetic" state in AdS/CFT
• Yangian Symmetry of String Theory on $Ad{S}_3\times S^3\times S^3\times S^1$ with Mixed 3-form Flux
• The Bethe Ansatz Equations for Reflecting Magnons
• On the anatomy of multi-spin magnon and single spike string solutions
• Yangian Symmetry at Two Loops for the su(2|1) Sector of N=4 SYM
• Reconstructing 1/2 BPS Space-Time Metrics from Matrix Models and Spin Chains
• Giant magnons and spiky strings on the conifold
• A note on oscillating strings in $Ad{S}_3\times S^3$ with mixed three-form fluxes
• The Leigh-Strassler Deformation and the Quest for Integrability
• Finite size corrections for open strings/open chains in planar AdS/CFT
• The generalised scaling function: a systematic study
• Strong coupling expansion of Baxter equation in N=4 SYM
• Full Lagrangian and Hamiltonian for quantum strings on AdS_4 x CP^3 in a near plane wave limit
• Semiclassical Quantization of the Giant Magnon
• Minimal solution of the AdS/CFT crossing equation
• Exploring the spectrum of planar $Ad{S}_4/CF{T}_3$ at finite coupling
• Resurgence of the dressing phase for ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$
• Superspin chains and supersymmetric gauge theories
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• On the Derivation of the Exact Slope Function
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• Review of AdS/CFT Integrability, Chapter II.2: Quantum Strings in AdS5xS5
• On the spectral problem of N=4 SYM with orthogonal or symplectic gauge group
• On circular strings in $(Ad{S}_3\times S^3{)}_{\varkappa }$
• Fermionic Correlators from Integrability
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• Semiclassical rigid strings with two spins in AdS_5
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• Structure of the string R-matrix
• Open Perturbatively Long-Range Integrable gl(N) Spin Chains
• Six-loop anomalous dimension of twist-two operators in planar N=4 SYM theory
• Toy models for wrapping effects
• Lifting asymptotic degeneracies with the Mirror TBA
• The 2-loop generalized scaling function from the BES/FRS equation
• Finite size corrections and integrability of $\mathcal{N}=2$ SYM and DLCQ strings on a pp-wave
• Quantum integrability of the Alday-Arutyunov-Frolov model
• On the Spectrum of the AdS_5xS^5 String at large lambda
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• Integrable Spin Chains on the Conformal Moose
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• The Bethe Ansatz for AdS5 x S5 Bound States
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• More about "short" spinning quantum strings
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• Issues on magnon reflection
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• On S-Matrix factorization of the Landau-Lifshitz model
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• Emergent Classical Strings from Matrix Model
• On twist-two operators in N=4 SYM
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• On the pulsating strings in AdS_4 x CP3
• ABJM quantum spectral curve and Mellin transform
• Giant Magnons under NS-NS and Melvin Fields
• Large spin expansion of the long-range Baxter equation in the sl(2) sector of N=4 SYM
• Exact solutions for N-magnon scattering
• Anomalous dimensions of finite size field strength operators in N=4 SYM
• Scattering amplitudes at strong coupling for 4K gluons
• Near Flat Space limit of strings on AdS_4 x CP^3
• Near-flat space limit and Einstein manifolds
• On the origin of the dressing phase in N=4 Super Yang-Mills
• The Leading Order Dressing Phase in ABJM Theory
• Quantum fluctuations of rotating strings in AdS_5 x S^5
• The S-matrix of the Faddeev-Reshetikhin Model, Diagonalizability and PT Symmetry
• Algebraic Curves for Integrable String Backgrounds
• Strings on the deformed T^{1,1}: giant magnon and single spike solutions
• Three-point functions at strong coupling in the BMN limit
• BPS Condensates, Matrix Models and Emergent String Theory
• TBA-like equations and Casimir effect in (non-)perturbative AdS/CFT
• Gauge Theories as String Theories: the First Results
• Testing the nested light-cone Bethe equations of the AdS_5 x S^5 superstring
• Strong coupling anomalous dimensions of $\mathcal{N}=4$ super Yang-Mills
• Review of AdS/CFT Integrability, Chapter I.2: The spectrum from perturbative gauge theory
• Spectral curve for open strings attached to the Y=0 brane
• From nesting to dressing
• Quantum Landau-Lifshitz model at four loops: 1/J and 1/J^2 corrections to BMN energies
• Spin chain for the deformed ABJM theory
• Is there a tower of charges to be discovered?
• N-body Dynamics of Giant Magnons in RxS2
• Asymptotic Bethe equations for open boundaries in planar AdS/CFT
• On the breakdown of perturbative integrability in large N matrix models
• Matrix Models, Complex Geometry and Integrable Systems. II
• Statistical mechanics for dilatations in N=4 super Yang--Mills theory
• Large-Spin and Large-Winding Expansions of Giant Magnons and Single Spikes
• The dual string sigma-model of the SU_q(3) sector
• Strong coupling from the Hubbard model
• On the massless modes of the AdS3/CFT2 integrable systems
• Approaching the BFKL pomeron via integrable classical solutions
• Superspace methods for the computation of wrapping effects in the standard and beta-deformed N=4 SYM
• Giant magnons and non-maximal giant gravitons
• Highest states in light-cone $Ad{S}_5\times S^5$ superstring
• Microscopic formulation of the S-matrix in AdS/CFT
• ABJM quantum spectral curve at twist 1: algorithmic perturbative solution
• On analytical perturbative solution of ABJM quantum spectral curve
• Giant Spinons
• On the dressing phase in the SL(2) Bethe Ansatz
• Quantum Strings and Bethe Equations
• Wrapping effects in supersymmetric gauge theories
• The Ising model and planar N=4 Yang-Mills
• Semiclassical Strings on Curved Branes
• Integrable systems and AdS/CFT duality
• Nonplanar Four-Loop Anomalous Dimensions of Twist-Two Operators in N=4 Super Yang-Mills Theory: Higher Moment, General Result, and Cusp Anomalous Dimension
• Integrable boundaries in AdS/CFT: revisiting the Z=0 giant graviton and D7-brane
• Comments on Correlation Functions of Large Spin Operators and Null Polygonal Wilson Loops
• A note on the Near Flat Limit for strings in the Maldacena-Nunez background
• PSU(2,2|4) Exchange Algebra of N=4 Superconformal Multiplets
• DGLAP and BFKL equations in $\mathcal{N}=4$ SYM: from weak to strong coupling
• Quantum deformation of cubic string field theory
• Classical Lie Bialgebras for AdS/CFT Integrability by Contraction and Reduction
• Time dynamics of Bethe ansatz solvable models
• Exact Results in Supersymmetric Gauge Theories
• Semiclassical Strings in Supergravity PFT
• Fermion zero modes for the mixed-flux AdS${}_3$ giant magnon
• The SU(2) Long Range Bethe Ansatz and Continuous Integrable Systems
• Gauge-String Dualities and Some Applications
• Including a phase in the Bethe equations of the Hubbard model
• High accuracy energy formulas for the attractive two-site Bose-Hubbard model
• Analytic Bethe Ansatz Solutions for Highest States in the su(1|1) and su(2) Sectors
• Yangian Symmetry, S-Matrices and Bethe Ansatz for the AdS5 x S5 Superstring
• The SU(1|2) and SU(2|2) Sectors from Superstrings in AdS5 x S5
• 12 loops and triple wrapping in ABJM theory from integrability
• Semiclassical quantization of the mixed-flux AdS${}_3$ giant magnon
• Large-Spin Expansions of Giant Magnons
• Unitarity methods for scattering in two dimensions
• Rotating and Orbiting Strings in Dp-brane background
• Classical limit of Quantum Sigma-Models from Bethe Ansatz
• Fermionic contribution to the anomalous dimension of twist-2 operators in N=4 SYM theory, critical indices and integrability
• On the singularities of the R-R AdS_3 x S^3 x T^4 S matrix
• AdS/CFT duality at strong coupling
• Orthogonality of Q-Functions up to Wrapping in Planar N=4 Super Yang-Mills Theory