Nambu-Goto Strings from $SU(\, N\,)$ Born-Infeld model

S. Ansoldi¹

Dipartimento di Fisica Teorica dell'Università,

Istituto Nazionale di Fisica Nucleare, Sezione di Trieste,

Strada Costiera 11, 34014-Trieste, Italy

C. Castro²

Center for Theoretical Studies of Physical Systems

Clark Atlanta University, Atlanta, GA30314

E. I. Guendelman³

Physics Department, Ben Gurion University,

Beer Sheva, Israel

E.Spallucci⁴

Dipartimento di Fisica Teorica dell'Università,

Istituto Nazionale di Fisica Nucleare, Sezione di Trieste,

Strada Costiera 11, 34014-Trieste, Italy

Abstract:

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.