The Near-Flat-Space and BMN Limits for Strings in AdS4 x CP3 at One Loop

TL;DR

This work analyzes one-loop corrections to strings in AdS$_4$ × CP$^3$ within the BMN and near-flat-space limits, deriving a simplified near-flat-space Lagrangian from a large worldsheet boost and testing quantum consistency by comparing with BMN results and the integrability-based dispersion relation. The authors compute mass shifts for light and heavy modes, uncover regulator-dependent extra terms, and demonstrate that near-flat-space results emerge as limits of the BMN calculations. They show the familiar $c = -\log 2 /(2\pi)$ piece in the light sector arises from tadpoles and discuss how different cutoff schemes affect this term, including the possibility of a zero-sum with the new prescription. The heavy modes exhibit mass non-coincidence and possible decay into light modes, highlighting interesting dynamical aspects of the spectrum beyond the simple BMN picture. Overall, the paper establishes one-loop quantum consistency of the near-flat-space truncation, clarifies regulator sensitivities, and connects to broader integrability-based results and related analyses at finite volume.

Abstract

This paper studies type IIA string theory in AdS4 x CP3 in both the BMN limit and the Maldacena-Swanson or near-flat-space limit. 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(lambda). Here we see agreement with the results of McLoughlin, Roiban & Tseytlin, and we observe that it does not appear to be possible to fully implement the cutoff suggested by Gromov & Mikhaylov, 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 regularisation.