Strings in AdS_4 x CP^3: finite size spectrum vs. Bethe Ansatz

Abstract

We compute the first curvature corrections to the spectrum of light-cone gauge type IIA string theory that arise in the expansion of $Ad{S}_4\times {\mathbb{CP}}^3$ about a plane-wave limit. The resulting spectrum is shown to match precisely, both in magnitude and degeneration that of the corresponding solutions of the all-loop Gromov--Vieira Bethe Ansatz. The one-loop dispersion relation correction is calculated for all the single oscillator states of the theory, with the level matching condition lifted. It is shown to have all logarithmic divergences cancelled and to leave only a finite exponentially suppressed contribution, as shown earlier for light bosons. We argue that there is no ambiguity in the choice of the regularization for the self-energy sum, since the regularization applied is the only one preserving unitarity. Interaction matrices in the full degenerate two-oscillator sector are calculated and the spectrum of all two light magnon oscillators is completely determined. The same finite-size corrections, at the order 1/J, where $J$ is the length of the chain, in the two-magnon sector are calculated from the all loop Bethe Ansatz. The corrections obtained by the two completely different methods coincide up to the fourth order in ${\lambda }^{\prime }=\lambda /J^2$. We conjecture that the equivalence extends to all orders in $\lambda$ and to higher orders in 1/J.

32 pages. Published version; journal reference added

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Cited by in corpus (16)

• Classical integrability and quantum aspects of the AdS(3) x S(3) x S(3) x S(1) superstring
• Near BMN dynamics of the AdS(3) x S(3) x S(3) x S(1) superstring
• Generalized cusp in AdS_4 x CP^3 and more one-loop results from semiclassical strings
• One Loop Amplitudes In ABJM
• Comment on Strings in AdS3 x S3 x S3 x S1 at One Loop
• Two-loop cusp anomaly in ABJM at strong coupling
• Eliminating ambiguities for quantum corrections to strings moving in $Ad{S}_4\times {\mathbb{CP}}^3$
• Classical and quantum integrability in AdS(2)/CFT(1)
• Numerical results for the exact spectrum of planar AdS4/CFT3
• Matching three-point functions of BMN operators at weak and strong coupling
• The Leading Order Dressing Phase in ABJM Theory
• Note on Integrability of Marginally Deformed ABJ(M) Theories
• Kaluza-Klein gauge and minimal integrable extension of OSp(4|6)/(SO(1,3) x U(3)) sigma-model
• Complete type IIA superstring action on IIA plane wave background
• Multi-Spin Strings in AdS_4*CP^3 and its β-deformation
• Worldsheet one-loop energy correction to IIA Giant Magnon