Infinite Dimensional Free Algebra and the Forms of the Master Field

Abstract

We find an infinite dimensional free algebra which lives at large N in any SU(N)-invariant action or Hamiltonian theory of bosonic matrices. The natural basis of this algebra is a free-algebraic generalization of Chebyshev polynomials and the dual basis is closely related to the planar connected parts. This leads to a number of free-algebraic forms of the master field including an algebraic derivation of the Gopakumar-Gross form. For action theories, these forms of the master field immediately give a number of new free-algebraic packagings of the planar Schwinger-Dyson equations.

39 pages. Expanded historical remarks

References in corpus (2)

• Gauge Theory Correlators from Non-Critical String Theory
• The Algebras of Large N Matrix Mechanics

Cited by in corpus (7)

• On the Integrability of large N Plane-Wave Matrix Theory
• Supersymmetric D3 brane and N=4 SYM actions in plane wave backgrounds
• Large N Matrix Mechanics on the Light-Cone
• Three types of statistics and the entropy bounds
• Supergrassmannian and large N limit of quantum field theory with bosons and fermions
• On the Large N Limit of Conformal Field Theory
• A Free-Algebraic Solution for the Planar Approximation