Large N Spectrum of two Matrices in a Harmonic Potential and BMN energies

Abstract

The large N spectrum of the quantum mechanical hamiltonian of two hermitean matrices in a harmonic potential is studied in a framework where one of the matrices is treated exactly and the other is treated as a creation operator impurity in the background of the first matrix. For the free case, the complete set of invariant eigenstates and corresponding energies are obtained. When g_{YM}^2 interactions are added, it is shown that the full string tension corrected spectrum of BMN loops is obtained.

arXiv comment26 pages

References in corpus (54)

• Large N Field Theories, String Theory and Gravity
• Strings in flat space and pp waves from $\mathcal{N}=4$ Super Yang Mills
• Bubbling AdS space and 1/2 BPS geometries
• The Dilatation Operator of Conformal N=4 Super Yang-Mills Theory
• Type IIB Green-Schwarz superstring in plane wave Ramond-Ramond background
• Invasion of the Giant Gravitons from Anti-de Sitter Space
• Giant Gravitons in Conformal Field Theory
• Large branes in AdS and their field theory dual
• A toy model for the AdS/CFT correspondence
• SUSY and Goliath
• Supersymmetric Gauge Theories and the AdS/CFT Correspondence
• Exact anomalous dimensions of {\cal N}=4 Yang-Mills operators with large R charge
• Exact Correlators of Giant Gravitons from dual N=4 SYM
• The Library of Babel: On the origin of gravitational thermodynamics
• A Matrix Big Bang
• D-branes in Yang-Mills theory and Emergent Gauge Symmetry
• Integrable open spin chains from giant gravitons
• Quantizing Open Spin Chains with Variable Length: an example from Giant Gravitons
• Plane-wave Matrix Theory from N=4 Super Yang-Mills on RxS^3
• Vibration modes of giant gravitons
• Long strings in two dimensional string theory and non-singlets in the matrix model
• All loop BMN state energies from matrices
• Fermions from Half-BPS Supergravity
• One-Dimensional String Theory with Vortices as Upside-Down Matrix Oscillator
• Giant Graviton Correlators from Dual SU(N) super Yang-Mills Theory
• Minisuperspace Quantization of "Bubbling AdS" and Free Fermion Droplets
• Giant Gravitons, BPS bounds and Noncommutativity
• Tracing the String: BMN correspondence at Finite J^2/N
• Classification of All 1/2 BPS Solutions of the Tiny Graviton Matrix Theory
• The Library of Babel
• Geometry Quantization from Supergravity: the case of "Bubbling AdS"
• Matrix Model Maps in AdS/CFT
• Giant gravitons in AdS/CFT (I): matrix model and back reaction
• Chronology Protection in anti-de Sitter
• Collective String Field Theory of Matrix Models in the BMN Limit
• LLL vs. LLM: Half BPS Sector of N=4 SYM Equals to Quantum Hall System
• Nonabelian Phenomena on D-branes
• Complex Matrix Model and Fermion Phase Space for Bubbling AdS Geometries
• Thermodynamics of R-charged Black Holes in AdS(5) From Effective Strings
• Bubbling AdS3
• Bubbling 1/4 BPS solutions in type IIB and supergravity reductions on S^n x S^n
• Towards the solution to the giant graviton puzzle
• Derivation of String Field Theory from the Large N BMN Limit
• Topology Changing Transitions in Bubbling Geometries
• Singularities and closed time-like curves in type IIB 1/2 BPS geometries
• Bubbling Orientifolds
• Collective field theory of the matrix-vector model
• SYM Description of SFT Hamiltonian in a PP-Wave Background
• c=1 Matrix Model from String Field Theory
• Revisiting the D1/D5 System or Bubbling in AdS_3
• 1/2 BPS Geometries of M2 Giant Gravitons
• Dynamics of Giant-Gravitons in the LLM geometry and the Fractional Quantum Hall Effect
• On Exponential corrections to the 1/N expansion in two-dimensional Yang Mills theory
• Holographic dynamics of unstable branes in AdS

Cited by in corpus (17)

• Branes, Anti-Branes and Brauer Algebras in Gauge-Gravity duality
• Giant Gravitons - with Strings Attached (III)
• Giant Gravitons - with Strings Attached (II)
• Giant Gravitons - with Strings Attached (I)
• A study of open strings ending on giant gravitons, spin chains and integrability
• Emergent geometry from q-deformations of N=4 super Yang-Mills
• Giant magnon bound states from strongly coupled N=4 SYM
• Free particles from Brauer algebras in complex matrix models
• Instantons, supersymmetric vacua, and emergent geometries
• BPS Operators in N=4 SYM: Calogero Models and 2D Fermions
• Strings on conifolds from strong coupling dynamics, part I
• Laplacians in polar matrix coordinates and radial fermionization in higher dimensions
• BPS Condensates, Matrix Models and Emergent String Theory
• 1/2 BPS Correlator and Free Fermion
• Strongly coupled large N spectrum of two matrices coupled via a Yang-Mills interaction
• Non supersymmetric strong coupling background from the large N quantum mechanics of two matrices coupled via a Yang-Mills interaction
• De Alfaro, Fubini and Furlan from multi Matrix Systems