Bulk geometry in gauge/gravity duality and color degrees of freedom

TL;DR

This paper challenges the belief that the ground-state wave function in gauge/gravity duality delocalizes at large N, showing instead that it remains localized and allowing the bulk geometry to be characterized by color degrees of freedom.

Contribution

It clarifies the meaning of matrix diagonalization in Yang-Mills theory, demonstrating that the ground-state wave function does not delocalize at large N, supporting the emergent space picture.

Findings

Ground-state wave function remains localized at large N

No conflict with bulk geometry locality

Diagonalization of matrices in Yang-Mills is more subtle than previously thought

Abstract

U($N$) supersymmetric Yang-Mills theory naturally appears as the low-energy effective theory of a system of $N$ D-branes and open strings between them. Transverse spatial directions emerge from scalar fields, which are $N\times N$ matrices with color indices; roughly speaking, the eigenvalues are the locations of D-branes. In the past, it was argued that this simple 'emergent space' picture cannot be used in the context of gauge/gravity duality, because the ground-state wave function delocalizes at large $N$, leading to a conflict with the locality in the bulk geometry. In this paper we show that this conventional wisdom is not correct: the ground-state wave function does not delocalize, and there is no conflict with the locality of the bulk geometry. This conclusion is obtained by clarifying the meaning of the 'diagonalization of a matrix' in Yang-Mills theory, which is not as obvious as one might think. This observation opens up the prospect of characterizing the bulk geometry via the color degrees of freedom in Yang-Mills theory, all the way down to the center of the bulk.