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

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Cited by in corpus (95)

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• Classical integrability and quantum aspects of the AdS(3) x S(3) x S(3) x S(1) superstring
• Two loop integrability for Chern-Simons theories with N=6 supersymmetry
• Exact Slope and Interpolating Functions in ABJM Theory
• Simplifying superstring and D-brane actions in AdS(4) x CP(3) superbackground
• Near BMN dynamics of the AdS(3) x S(3) x S(3) x S(1) superstring
• Dual Superconformal Symmetry of N=6 Chern-Simons Theory
• BPS Wilson loops and Bremsstrahlung function in ABJ(M): a two loop analysis
• Worldsheet spectrum in AdS(4)/CFT(3) correspondence
• ABJM models in N=3 harmonic superspace
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• Magnon dispersion to four loops in the ABJM and ABJ models
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• Light-cone gauge Hamiltonian for AdS_4 x CP^3 superstring
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• Giant Magnons on CP^3 by Dressing Method
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• On the Fermionic Frequencies of Circular Strings
• Semiclassical folded string in AdS4 X CP3
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• AdS_4 x CP^3 superstring and D=3 N=6 superconformal symmetry
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