Finite-size corrections for quantum strings on AdS_4 x CP^3

Abstract

We revisit the calculation of curvature corrections to the pp-wave energy of type IIA string states on AdS_4 x CP^3 initiated in arXiv:0807.1527. Using the near pp-wave Hamiltonian found in arXiv:0912.2257, we compute the first non-vanishing correction to the energy of a set of bosonic string states at order 1/R^2, where R is the curvature radius of the background. The leading curvature corrections give rise to cubic, order 1/R, and quartic, order 1/R^2, terms in the Hamiltonian, for which we implement the appropriate normal ordering prescription. Including the contributions from all possible fermionic and bosonic string states, we find that there exist logarithmic divergences in the sums over mode numbers which cancel between the cubic and quartic Hamiltonian. We show that the cubic Hamiltonian naturally requires that the cutoff for summing over heavy modes must be twice the one for light modes. With this prescription the strong-weak coupling interpolating function h(λ), entering the magnon dispersion relation, does not receive a one-loop correction, in agreement with the algebraic curve spectrum. However, the single magnon dispersion relation exhibits finite-size exponential corrections.

Published version, references added. A discussion on single oscillator states included

References in corpus (26)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Green-Schwarz action for Type IIA strings on $Ad{S}_4\times C{P}^3$
• Quantum corrections to the string Bethe ansatz
• The Bethe ansatz for superconformal Chern-Simons
• The all loop AdS4/CFT3 Bethe ansatz
• The Off-shell Symmetry Algebra of the Light-cone AdS_5 x S^5 Superstring
• Spin Chains in N=6 Superconformal Chern-Simons-Matter Theory
• Thermodynamic Bethe Ansatz for planar AdS/CFT: a proposal
• 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
• The AdS4/CFT3 algebraic curve
• Anomalous radius shift in AdS(4)/CFT(3)
• Integrable Spin Chain in Superconformal Chern-Simons Theory
• Two loop integrability for Chern-Simons theories with N=6 supersymmetry
• Finite-size corrections in the SU(2) x SU(2) sector of type IIA string theory on AdS_4 x CP^3
• Comment on the Scaling Function in AdS4 x CP3
• Superspace calculation of the four-loop spectrum in N=6 supersymmetric Chern-Simons theories
• Evidence for the classical integrability of the complete AdS(4) x CP(3) superstring
• Quantum Strings and the AdS4/CFT3 Interpolating Function
• Finite size giant magnons in the SU(2) x SU(2) sector of AdS_4 x CP^3
• Non-planar ABJM Theory and Integrability
• Finite-Size Corrections of the ${\mathbb{CP}}^3$ Giant Magnons: the Lüscher terms
• AdS/CFT v.s. String Loops
• Quantum finite-size effects for dyonic magnons in the AdS_4 x CP^3
• Peculiarities of String Theory on AdS(4) x CP(3)

Cited by in corpus (21)

• Classical integrability and quantum aspects of the AdS(3) x S(3) x S(3) x S(1) superstring
• Near BMN dynamics of the AdS(3) x S(3) x S(3) x S(1) superstring
• Generalized cusp in AdS_4 x CP^3 and more one-loop results from semiclassical strings
• Scattering Amplitudes/Wilson Loop Duality In ABJM Theory
• One Loop Amplitudes In ABJM
• Comment on Strings in AdS3 x S3 x S3 x S1 at One Loop
• Two-loop cusp anomaly in ABJM at strong coupling
• Macroscopic (and Microscopic) Massless Modes
• Worldsheet two- and four-point functions at one loop in AdS(3) / CFT(2)
• Scattering in ABJ theories
• Eliminating ambiguities for quantum corrections to strings moving in $Ad{S}_4\times {\mathbb{CP}}^3$
• Classical and quantum integrability in AdS(2)/CFT(1)
• Numerical results for the exact spectrum of planar AdS4/CFT3
• Strings in AdS_4 x CP^3: finite size spectrum vs. Bethe Ansatz
• The Leading Order Dressing Phase in ABJM Theory
• Note on Integrability of Marginally Deformed ABJ(M) Theories
• Integrability of N = 6 Chern-Simons Theory
• Kaluza-Klein gauge and minimal integrable extension of OSp(4|6)/(SO(1,3) x U(3)) sigma-model
• Complete type IIA superstring action on IIA plane wave background
• Multi-Spin Strings in AdS_4*CP^3 and its β-deformation
• Worldsheet one-loop energy correction to IIA Giant Magnon