The near-flat-space and BMN limits for strings in AdS4 × CP3 at one loop

Abstract

This paper studies type IIA string theory in AdS4 × CP3 in both the Berenstein–Maldacena–Nastase (BMN) and Maldacena–Swanson or near-flat-space limits. We derive the simpler Lagrangian for the latter limit by taking a large worldsheet boost of the BMN theory. We then calculate one-loop corrections to the correlators of the various fields using both theories. In all cases the near-flat-space results agree with a limit of the BMN results, providing evidence for the quantum consistency of this truncation. The corrections can also be compared to an expansion of the exact dispersion relation, known from integrability apart from one interpolating function h(λ). Here we see agreement with the results of McLoughlin et al (2008 J. High Energy Phys. JHEP11(2008)069), and observe that it does not appear to be possible to fully implement the cutoff suggested by Gromov & Mikhaylov (2009 J. High Energy Phys. JHEP04(2009)083), although for some terms we can do so. In both the near-flat-space and BMN calculations there are some extra terms in the mass shifts which break supersymmetry. These terms are extremely sensitive to the cutoff used, and can perhaps be seen as a consequence of using dimensional regularization.