1/J^2 corrections to BMN energies from the quantum long range Landau-Lifshitz model

Abstract

In a previous paper (hep-th/0509071), it was shown that quantum 1/J corrections to the BMN spectrum in an effective Landau-Lifshitz (LL) model match with the results from the one-loop gauge theory, provided one chooses an appropriate regularization. In this paper we continue this study for the conjectured Bethe ansatz for the long range spin chain representing perturbative planar N=4 Super Yang-Mills in the SU(2) sector, and the ``quantum string" Bethe ansatz for its string dual. The comparison is carried out for corrections to BMN energies up to 3rd order in the effective expansion parameter $\tl=λ/J^2$. After determining the ``gauge-theory'' LL action to order $\tl^3$, which is accomplished indirectly by fixing the coefficients in the LL action so that the energies of circular strings match with the energies found using the Bethe ansatz, we find perfect agreement. We interpret this as further support for an underlying integrability of the system. We then consider the ``string-theory'' LL action which is a limit of the classical string action representing fast string motion on an S^3 subspace of S^5 and compare the resulting $\tl^3/J^2$ corrections to the prediction of the ``string'' Bethe ansatz. As in the gauge case, we find precise matching. This indicates that the LL Hamiltonian supplemented with a normal ordering prescription and zeta-function regularization reproduces the full superstring result for the $1/J^2$ corrections, and also signifies that the string Bethe ansatz does describe the quantum BMN string spectrum to order $1/J^2$. We also comment on using the quantum LL approach to determine the non-analytic contributions in $\lambda$ that are behind the strong to weak coupling interpolation between the string and gauge results.

arXiv comment36 pages, v2: new Appendix C on non-analytic terms in the circular solution example added, v3: typos corrected

References in corpus (31)

• Strings in flat space and pp waves from $\mathcal{N}=4$ Super Yang Mills
• The Bethe-Ansatz for N=4 Super Yang-Mills
• A semi-classical limit of the gauge/string correspondence
• The N=4 SYM Integrable Super Spin Chain
• The Dilatation Operator of Conformal N=4 Super Yang-Mills Theory
• Semiclassical quantization of rotating superstring in AdS_5 x S^5
• Type IIB Green-Schwarz superstring in plane wave Ramond-Ramond background
• Bethe Ansatz for Quantum Strings
• Classical/quantum integrability in AdS/CFT
• Multi-spin string solutions in AdS_5 x S^5
• A Novel Long Range Spin Chain and Planar N=4 Super Yang-Mills
• The Factorized S-Matrix of CFT/AdS
• Spin chains and string theory
• Spinning strings in AdS_5 x S^5: new integrable system relations
• Planar N=4 gauge theory and the Inozemtsev long range spin chain
• Quantizing String Theory in AdS_5 X S^5: Beyond the pp-Wave
• Large spin limit of AdS_5 x S^5 string theory and low energy expansion of ferromagnetic spin chains
• Quantizing three-spin string solution in AdS_5 x S^5
• On Quantum Corrections to Spinning Strings and Bethe Equations
• Semiclassical relativistic strings in S^5 and long coherent operators in N=4 SYM theory
• Holography Beyond the Penrose Limit
• Matching quantum strings to quantum spins: one-loop vs. finite-size corrections
• On one-loop correction to energy of spinning strings in S^5
• Spinning strings in AdS_5 x S^5: one-loop correction to energy in SL(2) sector
• Strings in the near plane wave background and AdS/CFT
• Bethe Ansatz for a Quantum Supercoset Sigma Model
• BMN Operators and Superconformal Symmetry
• Higher Loops Beyond the SU(2) Sector
• N-Impurity Superstring Spectra Near the pp-Wave Limit
• Towards the exact dilatation operator of N=4 super Yang-Mills theory
• Spin Chain for Quantum Strings

Cited by in corpus (31)

• Quantum corrections to the string Bethe ansatz
• Two-loop world-sheet corrections in AdS_5 x S^5 superstring
• Uniform Light-Cone Gauge for Strings in AdS_5 x S^5: Solving su(1|1) Sector
• Logarithmic corrections to higher twist scaling at strong coupling from AdS/CFT
• Green-Schwarz Strings in TsT-transformed backgrounds
• Quantum spinning strings in AdS_4 x CP^3: testing the Bethe Ansatz proposal
• The AdS5xS5 Superstring in Light-Cone Gauge and its Bethe Equations
• Massive S-matrix of AdS_3 x S^3 x T^4 superstring theory with mixed 3-form flux
• Quantum corrections to spinning superstrings in AdS_3 x S^3 x M^4: determining the dressing phase
• Tailoring Three-Point Functions and Integrability II. Weak/strong coupling match
• Exact expressions for quantum corrections to spinning strings
• Bethe Ansatz in Stringy Sigma Models
• Double Scaling and Finite Size Corrections in sl(2) Spin Chain
• Nonperturbative scales in AdS/CFT
• Anisotropic Landau-Lifshitz sigma models from q-deformed AdS_5 x S^5 superstrings
• Asymptotic Bethe Ansatz S-matrix and Landau-Lifshitz type effective 2-d actions
• Holographic 3-point function at one loop
• Slow-string limit and "antiferromagnetic" state in AdS/CFT
• Two-loop AdS_5 x S^5 superstring: testing asymptotic Bethe ansatz and finite size corrections
• Review of AdS/CFT Integrability, Chapter II.2: Quantum Strings in AdS5xS5
• Integrable Spin Chains on the Conformal Moose
• Chaotic spin chains in AdS/CFT
• Finite-size corrections to the rotating string and the winding state
• More about "short" spinning quantum strings
• Semiclassical spectrum of a Jordanian deformation of $Ad{S}_5\times S^5$
• On string integrability. A journey through the two-dimensional hidden symmetries in the AdS/CFT dualities
• Quantum Landau-Lifshitz model at four loops: 1/J and 1/J^2 corrections to BMN energies
• Three-parameter deformation of $\mathbb{R}\times S^3$ in the Landau-Lifshitz limit
• On type 0 string theory in solvable RR backgrounds
• The $SU(2)$ Wess-Zumino-Witten spin chain sigma model
• The SU(1|2) and SU(2|2) Sectors from Superstrings in AdS5 x S5