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Journal Article

Quantum spinning strings in AdS(4) x CP3: testing the Bethe Ansatz proposal


McLoughlin,  Tristan
Duality & Integrable Structures, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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McLoughlin, T., Roiban, R., & Tseytlin, A. A. (2008). Quantum spinning strings in AdS(4) x CP3: testing the Bethe Ansatz proposal. Journal of high energy physics, 2008(11): 069. doi:10.1088/1126-6708/2008/11/069.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-1342-F
Recently, an asymptotic Bethe Ansatz that is claimed to describe anomalous dimensions of ``long'' operators in the planar Script N = 6 supersymmetric three-dimensional Chern-Simons-matter theory dual to quantum superstrings in AdS4 × Bbb CBbb P3 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 AdS5 × S5 case: a rigid circular string stretched in both AdS4 and along an S1 of Bbb CBbb P3 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 worldsheet space-like direction) and their Bethe Ansatz counterparts.