Giant Magnons in AdS4 x CP3: Embeddings, Charges and a Hamiltonian

Abstract

This paper studies giant magnons in CP3, which in all known cases are old solutions from S5 placed into two- and three-dimensional subspaces of CP3, namely CP1, RP2 and RP3. We clarify some points about these subspaces, and other potentially interesting three- and four-dimensional subspaces. After confirming that E-(J1-J4)/2 is a Hamiltonian for small fluctuations of the relevant 'vacuum' point particle solution, we use it to calculate the dispersion relation of each of the inequivalent giant magnons. We comment on the embedding of finite-J solutions, and use these to compare string solutions to giant magnons in the algebraic curve.

17 pages (plus appendices) and 1 figure. v2 has new discussion of placing finite-J giant magnons into CP^3, adds many references, and corrects a few typos

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• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Algebraic structures on parallel M2-branes
• Modeling Multiple M2's
• Comments on Multiple M2-branes
• Giant Magnons
• Superconformal Chern-Simons Theories and AdS_4/CFT_3 Correspondence
• Notes on Superconformal Chern-Simons-Matter Theories
• Green-Schwarz action for Type IIA strings on $Ad{S}_4\times C{P}^3$
• Comments on the Bagger-Lambert theory and multiple M2-branes
• Superstrings on AdS_4 x CP^3 as a Coset Sigma-model
• Finite-size Effects from Giant Magnons
• N=4 Superconformal Chern-Simons Theories with Hyper and Twisted Hyper Multiplets
• The Bethe ansatz for superconformal Chern-Simons
• The SU(2) x SU(2) sector in the string dual of N=6 superconformal Chern-Simons theory
• The all loop AdS4/CFT3 Bethe ansatz
• On Type IIA Penrose Limit and N=6 Chern-Simons Theories
• Pohlmeyer reduction of AdS_5 x S^5 superstring sigma model
• Magnon Bound States and the AdS/CFT Correspondence
• Wrapping at four loops in N=4 SYM
• Dyonic Giant Magnons
• N=6 super Chern-Simons theory S-matrix and all-loop Bethe ansatz equations
• Wrapping interactions at strong coupling -- the giant magnon
• Quantum spinning strings in AdS_4 x CP^3: testing the Bethe Ansatz proposal
• Semiclassical Quantization of Spinning Strings in AdS_4 x CP^3
• Spinning strings at one-loop in AdS_4 x P^3
• Anomalous dimension with wrapping at four loops in N=4 SYM
• The AdS4/CFT3 algebraic curve
• Infinite spin limit of semiclassical string states
• Integrable Spin Chain in Superconformal Chern-Simons Theory
• 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
• AdS4/CFT3 at One Loop
• Dressing the Giant Magnon
• One-loop corrections to Bagger-Lambert theory
• Pohlmeyer reduction revisited
• Single spike solutions for strings on S2 and S3
• Gauge invariant finite size spectrum of the giant magnon
• The AdS(5)xS(5) superstring quantum spectrum from the algebraic curve
• Finite-Size Effects for Dyonic Giant Magnons
• On reduced models for superstrings on AdS_n x S^n
• Quantum Wrapped Giant Magnon
• Magnons, their Solitonic Avatars and the Pohlmeyer Reduction
• Sine-Gordon-like action for the Superstring in AdS(5) x S(5)
• Finite size effects for giant magnons on physical strings
• Neumann-Rosochatius integrable system for strings on AdS_4 x CP^3
• Semi-classical strings in AdS_4*CP^3
• Efficient precision quantization in AdS/CFT
• Spiky Strings on AdS(4) X CP**3
• Finite size giant magnons in the SU(2) x SU(2) sector of AdS_4 x CP^3
• A new derivation of Luscher F-term and fluctuations around the giant magnon
• Finite-Size Effects for Multi-Magnon States
• Large Winding Sector of AdS/CFT
• Zero modes for the giant magnon
• Dual Spikes; New Spiky String Solutions
• A note on the reduction of the AdS4 x CP3 string sigma model
• Semiclassical Quantization of the Giant Magnon
• Giant Magnon and Spike Solutions with Two Spins in AdS4xCP3
• Giant Magnons and Singular Curves
• Finite-size Effects for Single Spike
• An alternative S-matrix for N=6 Chern-Simons theory ?
• Exact solutions for N-magnon scattering
• Spiky Strings in AdS(4) X CP**3 with Neveu-Schwarz Flux
• Near Flat Space limit of strings on AdS_4 x CP^3
• Vibrating giant spikes and the large-winding sector

Cited by in corpus (23)

• Simplifying superstring and D-brane actions in AdS(4) x CP(3) superbackground
• TBA and Y-system for planar $Ad{S}_4/CF{T}_3$
• Comment on Strings in AdS3 x S3 x S3 x S1 at One Loop
• Quantum Strings and the AdS4/CFT3 Interpolating Function
• Dyonic Giant Magnons in CP^3: Strings and Curves at Finite J
• Finite-size corrections for quantum strings on AdS_4 x CP^3
• Non-integrability and Chaos with Unquenched Flavor
• Spiky strings on AdS3 x S3 with NS-NS flux
• Full Lagrangian and Hamiltonian for quantum strings on AdS_4 x CP^3 in a near plane wave limit
• Strings in AdS_4 x CP^3: finite size spectrum vs. Bethe Ansatz
• On the spectral problem of N=4 SYM with orthogonal or symplectic gauge group
• Lessons from giant gravitons on $Ad{S}_5\times T^{1,1}$
• Scattering of Giant Magnons in CP^3
• Spiky Strings on I-brane
• Giant Magnons in Symmetric Spaces: Explicit N-soliton solutions for CP^n, SU(n) and S^n
• Rotating Strings in AdS(4) X CP(3) with B-NS holonomy
• Giant Spinons
• Wrapping effects in supersymmetric gauge theories
• Three Spin Spiky Strings in beta-deformed Background
• Divergent energy strings in $Ad{S}_5\times S^5$ with three angular momenta
• On Rotating and Oscillating Four-Spin Strings in AdS5 X S5
• Classical strings in $Ad{S}_4\times {\mathbb{CP}}^3$ with three angular momenta
• Some semiclassical structure constants for AdS_4 x CP^3