# Lattice QCD Link Variables Meaning of $\mu$ and $\nu$

I'm currently coding a lattice QCD project and ran into an issue with my understanding.

A link variable connecting two points could be in the $$\mu$$ or $$\nu$$ direction, for example, $$U_\mu(x)$$ goes from bottom left to bottom right on the diagram and $$U_\nu(x)$$ goes bottom left to top left, but what do these directions actually mean? Are both of these directions somehow along the same 1-D axis $$x$$? Or is $$\mu$$ is in the direction of the specified axis and $$\nu$$ is in the direction of time? (Both of these ideas do not work since you cannot go in two perpendicular directions on a 1-D line and $$\mu$$ and $$\nu$$ both apply to link variables with time; $$U_\mu(t)$$ and $$U_\nu(t)$$ exist)

It would also be great to know what 2-D slice of the 4-D lattice the diagram represents and the relative coordinates of the sites shown.

Diagram taken from https://fse.studenttheses.ub.rug.nl/20342/1/BRP_Thesis_Piter_Annema.pdf page 12

In this context $$x$$ labels a four-vector $$x=(x_0, x_1, x_2, x_3)$$ in euclidean spacetime and $$\mu$$ and $$\nu$$ label arbitrary spacetime directions (with $$\hat{\mu}$$ and $$\hat{\nu}$$ labeling the unit-vectors in those directions). In that sense the diagram you are referring to is representative of any 2-D slice out of the 4-D lattice.