Quantum spinning strings in AdS_4 x CP^3: testing the Bethe Ansatz proposal

Abstract

Recently, an asymptotic Bethe Ansatz that is claimed to describe anomalous dimensions of "long" operators in the planar N=6 supersymmetric three-dimensional Chern-Simons-matter theory dual to quantum superstrings in AdS_4 x CP^3 was proposed. It initially passed a few consistency checks but subsequent direct comparison to one-loop string-theory computations created some controversy. Here we suggest a resolution by pointing out that, contrary to the initial assumption based on the algebraic curve considerations, the central interpolating function h(λ) entering the BMN or magnon dispersion relation receives a non-zero one-loop correction in the natural string-theory computational scheme. We consider a basic example which has already played a key role in the AdS_5 x S^5 case: a rigid circular string stretched in both AdS_4 and along an S^1 of CP^3 and carrying two spins. Computing the leading one-loop quantum correction to its energy allows us to fix the constant one-loop term in h(λ) and also to suggest how one may establish a correspondence with the Bethe Ansatz proposal, including the non-trivial one-loop phase factor. We discuss some problems which remain in trying to match a part of world-sheet contributions (sensitive to compactness of the string direction) and their Bethe Ansatz counterparts.

37 pages; v2: references added and typos fixed

References in corpus (16)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Green-Schwarz action for Type IIA strings on $Ad{S}_4\times C{P}^3$
• The all loop AdS4/CFT3 Bethe ansatz
• Spin Chains in N=6 Superconformal Chern-Simons-Matter Theory
• Two-loop world-sheet corrections in AdS_5 x S^5 superstring
• Three-dimensional N=6 SCFT's and their membrane dynamics
• Logarithmic corrections to higher twist scaling at strong coupling from AdS/CFT
• Spinning strings at one-loop in AdS_4 x P^3
• The AdS4/CFT3 algebraic curve
• The Strong Coupling Limit of the Scaling Function from the Quantum String Bethe Ansatz
• Finite-size corrections in the SU(2) x SU(2) sector of type IIA string theory on AdS_4 x CP^3
• Spinning superstrings at two loops: strong-coupling corrections to dimensions of large-twist SYM operators
• Comment on the Scaling Function in AdS4 x CP3
• Semi-classical strings in AdS_4*CP^3
• Giant magnons in AdS_4/CFT_3: dispersion, quantization and finite--size corrections
• Quantum corrections to energy of short spinning string in AdS5

Cited by in corpus (13)

• Spinning strings at one-loop in AdS_4 x P^3
• Anomalous radius shift in AdS(4)/CFT(3)
• Comment on the Scaling Function in AdS4 x CP3
• Finite size giant magnons in the SU(2) x SU(2) sector of AdS_4 x CP^3
• Non-planar ABJM Theory and Integrability
• Two-loop test of the N=6 Chern-Simons theory S-matrix
• Dressed Giant Magnons on CP^3
• Giant Magnons on CP^3 by Dressing Method
• Weakly coupled N=4 Super Yang-Mills and N=6 Chern-Simons theories from u(2|2) Yangian symmetry
• Finite-Size Corrections of the ${\mathbb{CP}}^3$ Giant Magnons: the Lüscher terms
• Factorized Tree-level Scattering in AdS_4 x CP^3
• Comments on Baryon-like Operators in N=6 Chern-Simons-matter theory of ABJM
• The virtual scaling function of twist operators in the N=6 Chern-Simons theory