Zerobrane Matrix Mechanics, Monopoles and Membrane Approach in QCD

TL;DR

This paper proposes a T-dual matrix mechanics model of QCD where monopoles are represented as zerobranes, revealing confinement features and suggesting a membrane interpretation of large N QCD.

Contribution

It introduces a novel T-dual matrix quantum mechanics framework for QCD, linking monopoles, flux tubes, and membrane dynamics in a unified approach.

Findings

Linearly rising potential between zerobranes indicating flux tubes

Monopole condensation at enhanced gauge symmetry points

Large N QCD described as a membrane in five dimensions

Abstract

We conjecture that a T-dual form of pure QCD describes dynamics of point-like monopoles. T-duality transforms the QCD Lagrangian into a matrix quantum mechanics of zerobranes which we identify with monopoles. At generic points of the monopole moduli space the SU(N) gauge group is broken down to $U(1)^{N-1}$ reproducing the key feature of 't Hooft's Abelian projection. There are certain points in the moduli space where monopole positions coincide, gauge symmetry is enhanced and gluons emerge as massless excitations. We show that there is a linearly rising potential between zerobranes. This indicates the presence of a stretched flux tube between monopoles. The lowest energy state is achieved when monopoles are sitting on top of each other and gauge symmetry is enhanced. In this case they behave as free massive particles and can condense. In fact, we find a constant eigenfunction of the corresponding Hamiltonian which describes condensation of monopoles. Using the monopole quantum mechanics, we argue that large $N$ QCD in this T-dual picture is a theory of a closed bosonic membrane propagating in {\em five} dimensional space-time. QCD point-like monopoles can be regarded in this approach as constituents of the membrane.