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

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.

32 pages

References in corpus (8)

• Giant Magnons
• Green-Schwarz action for Type IIA strings on $Ad{S}_4\times C{P}^3$
• Finite-size Effects from Giant Magnons
• The AdS5xS5 Superstring in Light-Cone Gauge and its Bethe Equations
• Connecting giant magnons to the pp-wave: An interpolating limit of $Ad{S}_5\times S^5$
• Finite-size corrections in the SU(2) x SU(2) sector of type IIA string theory on AdS_4 x CP^3
• Near Flat Space limit of strings on AdS_4 x CP^3
• Off-shell symmetry algebra of the AdS_4 x CP^3 superstring

Cited by in corpus (8)

• Classical integrability and quantum aspects of the AdS(3) x S(3) x S(3) x S(1) superstring
• Worldsheet scattering in AdS(3)/CFT(2)
• Generalized cusp in AdS_4 x CP^3 and more one-loop results from semiclassical strings
• Macroscopic (and Microscopic) Massless Modes
• Worldsheet two- and four-point functions at one loop in AdS(3) / CFT(2)
• Eliminating ambiguities for quantum corrections to strings moving in $Ad{S}_4\times {\mathbb{CP}}^3$
• Dimensionally regularized Tsallis' Statistical Mechanics and two-body Newton's gravitation
• Dimensionally regularized Boltzmann-Gibbs Statistical Mechanics and two-body Newton's gravitation