Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1997-12-09
Nucl.Phys. B529 (1998) 656-688
Physics
High Energy Physics
High Energy Physics - Theory
44 pages, 8 eps figures, 3 tables, LaTeX2.09; this is the published version
Scientific paper
10.1016/S0550-3213(98)00461-1
We have discovered that the gauge invariant observables of matrix models invariant under U($N$) form a Lie algebra, in the planar large-N limit. These models include Quantum Chromodynamics and the M(atrix)-Theory of strings. We study here the gauge invariant states corresponding to open strings (`mesons'). We find that the algebra is an extension of a remarkable new Lie algebra ${\cal V}_{\Lambda}$ by a product of more well-known algebras such as $gl_{\infty}$ and the Cuntz algebra. ${\cal V}_{\Lambda}$ appears to be a generalization of the Lie algebra of vector fields on the circle to non-commutative geometry. We also use a representation of our Lie algebra to establish an isomorphism between certain matrix models (those that preserve `gluon number') and open quantum spin chains. Using known results on quantum spin chains, we are able to identify some exactly solvable matrix models. Finally, the Hamiltonian of a dimensionally reduced QCD model is expressed explicitly as an element of our Lie algebra.
Lee C.-W. H.
Rajeev Sarada. G.
No associations
LandOfFree
Symmetry Algebras of Large-N Matrix Models for Open Strings does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Symmetry Algebras of Large-N Matrix Models for Open Strings, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Symmetry Algebras of Large-N Matrix Models for Open Strings will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-437456