Emergent Classical Strings from Matrix Model

TL;DR

This paper demonstrates how classical string solutions, including giant magnons and folded strings, emerge from a matrix quantum mechanics model related to N=4 super Yang-Mills theory, revealing a deep connection between gauge theory and string theory.

Contribution

It introduces a framework where classical string configurations naturally arise from many-magnon states in a matrix model, extending previous ideas to include dyonic magnons and folded strings.

Findings

Classical string solutions are reproduced from matrix model states.

Bound string-bit configurations match giant magnon dispersion relations.

Emergence of folded/circular strings in infinite spin limits.

Abstract

Generalizing the idea of hep-th/0509015 by Berenstein, Correa, and Vazquez, we study many-magnon states in an SU(2) sector of a reduced matrix quantum mechanics obtained from N=4 SU(N) super Yang-Mills on R x S^3. Generic Q-magnon states are described as a chain of ``string-bits'' joining Q+1 eigenvalues of background matrices which form a 1/2 BPS circular droplet in the large N limit. We will concentrate on infinitely long states whose first and last eigenvalues localize at the edge of the droplet. Each constituent string-bit has a complex quasi-momentum in general, while the total quasi-momentum P of the state is real. For given Q and P, the minimum energy of the chain of string-bits is realized when the Q+1 eigenvalues are equally spaced on one and the same line segment joining the two outmost eigenvalues localized on the edge with angular difference P. Such configuration of bound string-bits precisely reproduces the dispersion relation for dyonic giant magnons in classical string theory. We also show the emergence of two-spin folded/circular strings in special infinite spin limit as particular configurations of closed chains of string-bits.