Finite-size corrections in the SU(2) x SU(2) sector of type IIA string theory on AdS_4 x CP^3

Abstract

We consider finite-size corrections in the SU(2) x SU(2) sector of type IIA string theory on AdS_4 x CP^3, which is the string dual of the recently constructed N=6 superconformal Chern-Simons theory of Aharony, Bergman, Jafferis and Maldacena (ABJM theory). The string states we consider are in the R x S^2 x S^2 subspace of AdS_4 x CP^3 with an angular momentum J on CP^3 being large. We compute the finite-size corrections using two different methods, one is to consider curvature corrections to the Penrose limit giving an expansion in 1/J, the other by considering a low energy expansion in lambda'=lambda/J^2 of the string theory sigma-model, lambda being the 't Hooft coupling of the dual ABJM theory. For both methods there are interesting issues to deal with. In the near-pp-wave method there is a 1/\sqrt{J} interaction term for which we use zeta-function regularization in order to compute the 1/J correction to the energy. For the low energy sigma-model expansion we have to take into account a non-trivial coupling to a non-dynamical transverse direction. We find agreement between the two methods. At order lambda' and lambda'^2, for small lambda', our results are analogous to the ones for the SU(2) sector in type IIB string theory on AdS_5 x S^5. Instead at order lambda'^3 there are interactions between the two two-spheres. We compare our results with the recently proposed all-loop Bethe ansatz of Gromov and Vieira and find agreement.

21 pages. v2: typos fixed, refs. added. v3: misprints corrected, refs. added

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Cited by in corpus (32)

• Quantum spinning strings in AdS_4 x CP^3: testing the Bethe Ansatz proposal
• Spinning strings at one-loop in AdS_4 x P^3
• The complete AdS(4) x CP(3) superspace for the type IIA superstring and D-branes
• Anomalous radius shift in AdS(4)/CFT(3)
• Two loop integrability for Chern-Simons theories with N=6 supersymmetry
• Comment on the Scaling Function in AdS4 x CP3
• Superspace calculation of the four-loop spectrum in N=6 supersymmetric Chern-Simons theories
• Magnons, their Solitonic Avatars and the Pohlmeyer Reduction
• Two-loop cusp anomaly in ABJM at strong coupling
• Finite size giant magnons in the SU(2) x SU(2) sector of AdS_4 x CP^3
• Topological branes, p-algebras and generalized Nahm equations
• Non-planar ABJM Theory and Integrability
• Correlation functions of magnon and spike
• A New and Elementary CP^n Dyonic Magnon
• Hydrodynamics of N=6 Superconformal Chern-Simons Theories at Strong Coupling
• A note on the reduction of the AdS4 x CP3 string sigma model
• Correlation function of dyonic strings
• Giant Magnons on CP^3 by Dressing Method
• Dressed Giant Magnons on CP^3
• On semiclassical calculation of three-point functions in AdS_4 x CP^3
• Finite-Size Corrections of the ${\mathbb{CP}}^3$ Giant Magnons: the Lüscher terms
• D2 to M2 Procedure for D2-Brane DBI Effective Action
• Factorized Tree-level Scattering in AdS_4 x CP^3
• On Three-point Functions in the AdS_4/CFT_3 Correspondence
• Near Flat Space limit of strings on AdS_4 x CP^3
• Squashing Gravity Dual of N=6 Superconformal Chern-Simons Gauge Theory
• Spiky Strings in AdS(4) X CP**3 with Neveu-Schwarz Flux
• Zero Modes for the Boundary Giant Magnons
• Membrane Dynamics in Three dimensional N=6 Supersymmetric Chern-Simons Theory
• Semiclassical strings in AdS(3) X S^2
• Correlation functions of the ABJM model
• Fermionic reductions of the AdS4 x CP3 superstring