  We study the probabilities with which chordal Schramm-Loewner Evolutions
(SLE) visit small neighborhoods of boundary points. We find formulas for
general chordal SLE boundary visiting probability amplitudes, also known as SLE
boundary zig-zags or order refined SLE multi-point Green's functions on the
boundary. Remarkably, an exact answer can be found to this important SLE
question for an arbitrarily large number of marked points. The main technique
employed is a spin chain-Coulomb gas correspondence between tensor product
representations of a quantum group and functions given by Dotsenko-Fateev type
integrals. We show how to express these integral formulas in terms of
regularized real integrals, and we discuss their numerical evaluation.
  The results are universal in the sense that apart from an overall
multiplicative constant the same formula gives the amplitude for many different
formulations of the SLE boundary visit problem. The formula also applies to
renormalized boundary visit probabilities for interfaces in critical lattice
models of statistical mechanics: we compare the results with numerical
simulations of percolation, loop-erased random walk, and Fortuin-Kasteleyn
random cluster models at Q=2 and Q=3, and find good agreement.
