Zero-brane matrix mechanics, monopoles and membrane approach in QCD

We conjecture that a T-dual form of pure QCD describes dynamics of point-li ke monopoles. T-duality transforms the QCD Lagrangian into a matrix quantum mechanics of zero-branes which we identify with monopoles. At generic poin ts 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 sh ow that there is a linearly rising potential between zero-branes. This indi cates the presence of a stretched flux tube between monopoles. The lowest e nergy 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 parti cles and can be condensed. 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 p icture is a theory of a closed bosonic membrane propagating in five-dimensi onal space-time. QCD point-like monopoles can be regarded in this approach as constituents of the membrane.