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

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

2008-07-09

arxiv.org/abs/0807.1527v3

Nucl.Phys.B810:150-173,2009

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1016/j.nuclphysb.2008.10.020

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.

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