Membranes and Matrix Models

Abstract

Section I contains introductory remarks about surface motions. Section II gives a detailed derivation of $H=-\Delta -Tr{\sum }_{i<j}[X_i,X_j{]}^2$ as describing a quantized discrete analogue of relativistically invariant membrane dynamics. Section III concerns the question of zero-energy bound-states in SU(N)-invariant supersymmetric matrix models. Section IV discusses the space of solutions of some differential matrix equations on $(-\infty ,+\infty )$, interpolating between different representations of $su(2)$. Some exercises are added, and one remark/conjecture concerning 5-commutators.

References in corpus (4)

• Matrix Perturbation Theory For M-theory On a PP-Wave
• Asymptotic Form of Zero Energy Wave Functions in Supersymmetric Matrix Models
• On The Construction of Zero Energy States in Supersymmetric Matrix Models III
• Vanishing index for supersymmetric 2-matrix model with odd dimensional gauge group

Cited by in corpus (26)

• n-ary algebras: a review with applications
• Supersymmetric objects in the M-theory on a pp-wave
• Massive super Yang-Mills quantum mechanics: classification and the relation to supermembrane
• 5D action for longitudinal five branes on a pp-wave
• Construction of the Zero-Energy State of SU(2)-Matrix Theory: Near the Origin
• Fundamental Structures of M(brane) Theory
• Gauge Theory on Twisted $\kappa$-Minkowski: Old Problems and Possible Solutions
• Matrix Models and Lorentz Invariance
• Exact solutions for U(1) globally invariant membranes
• Lorentz-invariant membranes and finite matrix approximations
• Towards the Ground State of the Supermembrane
• Spiky membranes
• Noncritical osp(1|2,R) M-theory matrix model with an arbitrary time dependent cosmological constant
• U(1) invariant Membranes and Singularities
• M-brane dynamical symmetry and quantization
• Octonionic twists for supermembrane matrix models
• Partial Hamiltonian reduction of relativistic extended objects in light-cone gauge
• A dynamical symmetry for supermembranes
• Uniqueness of the coordinate independent Spin(9)xSU(2) state of Matrix Theory
• Matrix regularization of embedded 4-manifolds
• Diffeomorphism Algebra Structure and Membrane Theory
• Compactness and convexity results for closed relativistic strings
• Variational orthogonalization
• Quantum Dynamics on the Worldvolume from Classical su(n) Cohomology
• Aspects of noncommutativity in field theory, strings and membranes
• Optimized Fock space in the large N limit of quartic interactions in Matrix Models