  We prove a strong large deviation principle (LDP) for multiple chordal
SLE$_{0+}$ curves with respect to the Hausdorff metric. In the single-chord
case, this result strengthens an earlier partial result by the second author.
We also introduce a Loewner potential, which in the smooth case has a simple
expression in terms of zeta-regularized determinants of Laplacians. This
potential differs from the LDP rate function by an additive constant depending
only on the boundary data, that satisfies PDEs arising as a semiclassical limit
of the Belavin-Polyakov-Zamolodchikov equations of level two in conformal field
theory with central charge $c \to -\infty$.
  Furthermore, we show that every multichord minimizing the potential in the
upper half-plane for given boundary data is the real locus of a rational
function and is unique, thus coinciding with the $\kappa \to 0+$ limit of the
multiple SLE$_\kappa$. As a by-product, we provide an analytic proof of the
Shapiro conjecture in real enumerative geometry, first proved by Eremenko and
Gabrielov: if all critical points of a rational function are real, then the
function is real up to post-composition by a M\"obius transformation.
