On Asymptotic Hamiltonian for SU(N) Matrix Theory

Abstract

We compute the leading contribution to the effective Hamiltonian of SU(N) matrix theory in the limit of large separation. We work with a gauge fixed Hamiltonian and use generalized Born-Oppenheimer approximation, extending the recent work of Halpern and Schwartz for SU(2). The answer turns out to be a free Hamiltonian for the coordinates along the flat directions of the potential. Applications to finding ground state candidates and calculation of the correction (surface) term to Witten index are discussed.

13 pages, Latex; v2: a reference added; v3: References to the papers by M.B. Green and M. Gutperle are added. The complete calculation of the Witten index for SU(N) matrix theory follows from combination of the results of our paper with the results of M.B. Green and M. Gutperle and the results obtained by G. Moore, N. Nekrasov, and S. Shatashvili

References in corpus (5)

• D-particle bound states and generalized instantons
• Asymptotic Search for Ground States of SU(2) Matrix Theory
• D-instanton partition functions
• On the quantum mechanics of M(atrix) theory
• On the Construction of Zero Energy States in Supersymmetric Matrix Models

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• Normalized Vacuum States in N = 4 Supersymmetric Yang--Mills Quantum Mechanics with Any Gauge Group
• Asymptotic Form of Zero Energy Wave Functions in Supersymmetric Matrix Models
• On Stable Sector in Supermembrane Matrix Model
• Large N behavior of two dimensional supersymmetric Yang-Mills quantum mechanics
• Zero Energy States for SU(N): A Simple Exercise in Group Theory ?
• Asymptotic Factorisation of the Ground-State for SU(N)-invariant Supersymmetric Matrix-Models
• Spiky membranes
• Octonionic twists for supermembrane matrix models
• Light-cone SU(2) Yang-Mills theory and conformal mechanics
• On the Ground State Wave Function of Matrix Theory
• Uniqueness of the coordinate independent Spin(9)xSU(2) state of Matrix Theory
• Optimized Fock space in the large N limit of quartic interactions in Matrix Models