Neumann-Rosochatius system for strings in ABJ Model

Abstract

Neumann-Rosochatius system is a well known one dimensional integrable system. We study the rotating and pulsating string in $Ad{S}_4\times {\mathbb{CP}}^3$ with a $B_{\mathrm{NS}}$ holonomy turned on over ${\mathbb{CP}}^1\subset {\mathbb{CP}}^3$, or the so called Aharony-Bergman-Jafferis (ABJ) background. We observe that the string equations of motion in both cases are integrable and the Lagrangians reduce to a form similar to that of deformed Neuman-Rosochatius system. We find out the scaling relations among various conserved charges and comment on the finite size effect for the dyonic giant magnons on $R_t\times {\mathbb{CP}}^3$ with two angular momenta. For the pulsating string we derive the energy as function of oscillation number and angular momenta along ${\mathbb{CP}}^3$.

arXiv comment20 pages, several typos corrected. Better presented. Added references. To appear in JHEP

References in corpus (37)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• The Bethe-Ansatz for N=4 Super Yang-Mills
• A semi-classical limit of the gauge/string correspondence
• The N=4 SYM Integrable Super Spin Chain
• Fractional M2-branes
• The Complete One-Loop Dilatation Operator of N=4 Super Yang-Mills Theory
• Spinning strings in AdS_5 x S^5 and integrable systems
• Spinning strings in AdS_5 x S^5: new integrable system relations
• Circular Semiclassical String Solutions on AdS_5 x S_5
• Dyonic Giant Magnons
• Yang-Mills Duals for Semiclassical Strings
• Spiky strings and giant magnons on S5
• 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
• Finite-Size Effects for Dyonic Giant Magnons
• Pulsating Strings on AdS_5 x S^5
• Semi-classical strings in AdS_4*CP^3
• Neumann-Rosochatius integrable system for strings on AdS_4 x CP^3
• Generalized pulsating strings
• Spinning Pulsating String Solitons in AdS_5 x S^5
• Integrable Spin Chain of Superconformal U(M)xU(N) Chern-Simons Theory
• Spinning strings in AdS_3 x S^3 with NS-NS flux
• Finite-size effects of Membranes on AdS_4 x S_7
• Improved Stability for Pulsating Multi-Spin String Solitons
• Finite-size Effect of the Dyonic Giant Magnons in N=6 super Chern-Simons Theory
• Spinning strings in the $\eta$-deformed Neumann-Rosochatius system
• Integrability of the eta-deformed Neumann-Rosochatius model
• Beyond the Planar Limit in ABJM
• Pulsating strings with mixed three-form flux
• Pulsating Strings With Angular Momenta
• On the pulsating strings in AdS_4 x CP3
• Spiky Strings in AdS(4) X CP**3 with Neveu-Schwarz Flux
• Nonplanar Integrability and Parity in ABJ Theory
• Finite-size Giant Magnons on AdS_4 x CP^3_γ
• Pulsating strings from two dimensional CFT on $(T^4{)}^N/S(N)$

Cited by in corpus (3)

• Neumann-Rosochatius system for (m,n) string in $Ad{S}_3\times S^3$ with mixed flux
• Neumann-Rosochatius system for strings on I-brane
• Neumann-Rosochatius system for rotating strings in $Ad{S}_3\times S^3\times S^3\times S^1$ with flux