From SYM Perturbation Theory to Closed Strings in Matrix Theory

TL;DR

This paper explores a Matrix theory framework for SYM on D4-branes that unifies perturbative gauge theory and closed string descriptions, providing insights into the AdS/CFT correspondence across all couplings.

Contribution

It introduces a Matrix theory approach based on Nahm equations that interpolates between SYM perturbation theory and closed string theory, revealing how world-sheet holes form closed surfaces.

Findings

Demonstrates a unified description valid for all 't Hooft couplings.

Shows explicit transition from holes in world-sheets to closed surfaces.

Provides a potential bridge between gauge theory and string theory regimes.

Abstract

For the purpose of better understanding the AdS/CFT correspondence it is useful to have a description of the theory for all values of the 't Hooft coupling, and for all $N$. We discuss such a description in the framework of Matrix theory for SYM on D4-branes, which is given in terms of quantum mechanics on the moduli space of solutions of the Nahm equations. This description reduces to both SYM perturbation theory and to closed string perturbation theory, each in its appropriate regime of validity, suggesting a way of directly relating the variables in the two descriptions. For example, it shows explicitly how holes in the world-sheets of the 't Hooft expansion close to give closed surfaces.