Coset construction of AdS particle dynamics

Abstract

We analyze dynamics of the AdS${}_{N+1}$ particle realized on the coset SO$(2,N)/$SO$(1,N)$. Hamiltonian reduction provides the physical phase space in terms of the coadjoint orbit obtained by boosting a timelike element of $\mathfrak{s}o(2,N)$. We show equivalence of this approach to geometric quantization and to the SO$(N)$ covariant oscillator description, for which the boost generators entail a complicated operator ordering. As an alternative scheme, we introduce dual oscillator variables and derive their algebra at the classical and the quantum level. This simplifies the calculations of the commutators for the boost generators and leads to unitary irreducible representations of $\mathfrak{s}o(2,N)$ for all admissible values of the mass parameter. We furthermore discuss an SO$(N)$ covariant supersymmetric extensions of the oscillator quantization, with its realization for superparticles in AdS${}_2$ and AdS${}_3$ given by recent works.

arXiv comment21+1 pages; v2: typos corrected, references updated; v3: minor changes, matches published version

References in corpus (44)

• Large N Field Theories, String Theory and Gravity
• Strings in flat space and pp waves from $\mathcal{N}=4$ Super Yang Mills
• Review of AdS/CFT Integrability: An Overview
• A semi-classical limit of the gauge/string correspondence
• Semiclassical quantization of rotating superstring in AdS_5 x S^5
• Multi-spin string solutions in AdS_5 x S^5
• Foundations of the AdS_5 x S^5 Superstring. Part I
• Integrability for the Full Spectrum of Planar AdS/CFT II
• Integrability for the Full Spectrum of Planar AdS/CFT
• Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model
• Quantum spectral curve for AdS_5/CFT_4
• Spinning strings in AdS_5 x S^5 and integrable systems
• Green-Schwarz String in AdS_5 x S^5: Semiclassical Partition Function
• Integrability and the AdS(3)/CFT(2) correspondence
• Light-cone Superstring in AdS Space-time
• Thermodynamic Bethe Ansatz for planar AdS/CFT: a proposal
• Strings on Semisymmetric Superspaces
• Review of AdS/CFT Integrability, Chapter IV.3: N=6 Chern-Simons and Strings on AdS4xCP3
• Giant magnons in the D1-D5 system
• Towards integrability for AdS3/CFT2
• Superstrings in AdS(2)xS(2)xT(6)
• Light cone gauge formulation of IIB supergravity in $Ad{S}_5\times S^5$ background and AdS/CFT correspondence
• An Integrability Primer for the Gauge-Gravity Correspondence: an Introduction
• Many-particle mechanics with D(2,1;alpha) superconformal symmetry
• N=2 superparticle near horizon of extreme Kerr-Newman-AdS-dS black hole
• More on integrable structures of superstrings in AdS(4) x CP(3) and AdS(2) x S(2) x T(6) superbackgrounds
• Particle dynamics near extreme Kerr throat and supersymmetry
• Anti-de Sitter particles and manifest (super)isometries
• Quantization of a relativistic particle on the SL(2,R) manifold based on Hamiltonian reduction
• N=2 supersymmetric particle near extreme Kerr throat
• On the Spectrum of the AdS_5xS^5 String at large lambda
• Bosonic String Quantization in Static Gauge
• Exact Quantization of a Superparticle in AdS_5 x S^5
• Static Gauge and Energy Spectrum of Single-mode Strings in AdS_5xS^5
• Orbit method quantization of the AdS${}_2$ superparticle
• Oscillator quantization of the massive scalar particle dynamics on AdS spacetime
• Isometry Group Orbit Quantization of Spinning Strings in AdS_3 x S^3
• Quantization of AdS x S particle in static gauge
• On particle dynamics in AdS_{N+1} space-time
• Superconformal SU(1,1|n) mechanics
• Higher-derivative N=4 superparticle in three-dimensional spacetime
• Coordinate representation of particle dynamics in AdS and in generic static spacetimes
• Spacecone quantization of AdS superparticle
• Higher-derivative superparticle in AdS${}_3$ space

Cited by in corpus (3)

• Couplings in D(2,1;a) superconformal mechanics from the SU(2) perspective
• Twistor description of spinning particles in AdS
• Super 0--brane action on the coset space of $D(2,1;\alpha )$ supergroup