Full Lagrangian and Hamiltonian for quantum strings on AdS_4 x CP^3 in a near plane wave limit

Abstract

We find the full interacting Lagrangian and Hamiltonian for quantum strings in a near plane wave limit of AdS_4 x CP^3. The leading curvature corrections give rise to cubic and quartic terms in the Lagrangian and Hamiltonian that we compute in full. The Lagrangian is found as the type IIA Green-Schwarz superstring in the light-cone gauge employing a superspace construction with 32 grassmann-odd coordinates. The light-cone gauge for the fermions is non-trivial since it should commute with the supersymmetry condition. We provide a prescription to properly fix the kappa-symmetry gauge condition to make it consistent with light-cone gauge. We use fermionic field redefinitions to find a simpler Lagrangian. To construct the Hamiltonian a Dirac procedure is needed in order to properly keep into account the fermionic second class constraints. We combine the field redefinition with a shift of the fermionic phase space variables that reduces Dirac brackets to Poisson brackets. This results in a completely well-defined and explicit expression for the full interacting Hamiltonian up to and including terms quartic in the number of fields.

40 pages. v2: Typos fixed, Refs. added

References in corpus (29)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Green-Schwarz action for Type IIA strings on $Ad{S}_4\times C{P}^3$
• The Bethe ansatz for superconformal Chern-Simons
• The all loop AdS4/CFT3 Bethe ansatz
• Spin Chains in N=6 Superconformal Chern-Simons-Matter Theory
• Three-dimensional N=6 SCFT's and their membrane dynamics
• 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
• String instanton in AdS(4)xCP(3)
• Magnon dispersion to four loops in the ABJM and ABJ models
• Comment on the Scaling Function in AdS4 x CP3
• Matching the Hagedorn temperature in AdS/CFT
• Finite size giant magnons in the SU(2) x SU(2) sector of AdS_4 x CP^3
• Non-planar ABJM Theory and Integrability
• One-Loop Corrections to Type IIA String Theory in AdS4 x CP3
• Light-cone gauge Hamiltonian for AdS_4 x CP^3 superstring
• Dressed Giant Magnons on CP^3
• Integrability of N=6 Chern-Simons Theory at Six Loops and Beyond
• Finite-Size Corrections of the ${\mathbb{CP}}^3$ Giant Magnons: the Lüscher terms
• Factorized Tree-level Scattering in AdS_4 x CP^3
• Two-Loop Spectroscopy of Short ABJM Operators
• Scattering of Giant Magnons in CP^3
• Emergent geometry in N=6 Chern-Simons-matter theory

Cited by in corpus (21)

• Review of AdS/CFT Integrability, Chapter IV.3: N=6 Chern-Simons and Strings on AdS4xCP3
• Generalized cusp in AdS_4 x CP^3 and more one-loop results from semiclassical strings
• Quantum Strings and the AdS4/CFT3 Interpolating Function
• More on integrable structures of superstrings in AdS(4) x CP(3) and AdS(2) x S(2) x T(6) superbackgrounds
• Correlation functions of magnon and spike
• Finite-size corrections for quantum strings on AdS_4 x CP^3
• Correlation function of dyonic strings
• The worldsheet low-energy limit of the AdS_4 x CP^3 superstring
• 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
• Finite size effect on the magnon's correlation functions
• On string integrability. A journey through the two-dimensional hidden symmetries in the AdS/CFT dualities
• New Penrose Limits and AdS/CFT
• Note on Integrability of Marginally Deformed ABJ(M) Theories
• Peculiarities of String Theory on AdS(4) x CP(3)
• Integrability of N = 6 Chern-Simons Theory
• Correlation functions of the ABJM 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