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

TL;DR

This paper introduces a new matrix model linking SU(N) gauge theories to Nambu-Goto string models, enabling a smooth transition between different string formulations and extending to p-branes in higher dimensions.

Contribution

It proposes an extended matrix model that connects gauge theories with Nambu-Goto strings through an auxiliary matrix field, bridging previous gaps in string representation.

Findings

The model smoothly interpolates between Schild and Nambu-Goto strings.

The matrix variable acts as a world-sheet auxiliary field in the large-N limit.

Extension to p-branes is possible with increased target space dimensions.

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.