Nambu–Goto Strings from SU( N ) Born-Infeld model

The spectrum of quenched Yang-Mills theory in the large–N limit displays strings and higher dimensional extended objects. The effective dynamics of string-like excitations is encoded into area preserving Schild action. In this letter, we bridge the gap between SU(N ) gauge models and fully reparametrization invariant Nambu–Goto string models by introducing an extra matrix degree of freedom in the Yang-Mills action. In the large–N limit this matrix variable becomes the world-sheet auxiliary field allowing a smooth transition between the Schild and Nambu–Goto strings. The new improved matrix model we propose here can be extended to p-branes provided we enlarge the dimensionality of the target spacetime.