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We give new descriptions of lattice SU(N) Yang-Mills theory in terms of newlattice variables. The validity of such descriptions has already beendemonstrated in the SU(2) Yang-Mills theory by our previous works from theviewpoint of defining and extracting topological degrees of freedom such asgauge-invariant magnetic monopoles and vortices which play the dominant role inquark confinement. In particular, we have found that the SU(3) latticeYang-Mills theory has two possible options, maximal and minimal: The existenceof the minimal option has been overlooked so far, while the maximal optionreproduces the conventional SU(3) Cho-Faddeev-Niemi-Shabanov decomposition inthe naive continuum limit. The new description gives an important framework forunderstanding the mechanism of quark confinement based on the dualsuperconductivity.

New descriptions of lattice SU(N) Yang-Mills theory towards quark confinement