Coordinate/Field Duality in Gauge Theories: Emergence of Matrix Coordinates

TL;DR

This paper explores how the coordinate/field duality in gauge theories leads to matrix-valued dual coordinates in non-Abelian cases, aligning with string theory concepts and providing insights into internal dynamics of confined states.

Contribution

It extends the coordinate/field duality to non-Abelian gauge theories, showing dual coordinates become matrices consistent with lattice gauge theory and string theory frameworks.

Findings

Dual coordinates in non-Abelian gauge theories are matrices.

Matrix coordinates correspond to bound states of D0-branes.

In the unbroken phase, matrix coordinates describe internal dynamics of confined states.

Abstract

The proposed coordinate/field duality [Phys. Rev. Lett. 78 (1997) 163] is applied to the gauge and matter sectors of gauge theories. In the non-Abelian case, due to indices originated from the internal space, the dual coordinates appear to be matrices. The dimensions and the transformations of the matrix coordinates of gauge and matter sectors are different and are consistent to expectations from lattice gauge theory and the theory of open strings equipped with the Chan-Paton factors. It is argued that in the unbroken symmetry phase, where only proper collections of field components as colorless states are detected, it is logical to assume that the same happens for the dual coordinates, making matrix coordinates the natural candidates to capture the internal dynamics of baryonic confined states. The proposed matrix coordinates happen to be the same appearing in the bound-state of D0-branes of string theory.