  In this article, we give an explicit relationship of SLE partition functions
with Coulomb gas formalism of conformal field theory. We first construct a
family of SLE${}_\kappa$ partition functions as Coulomb gas integrals and
derive their various properties. In accordance with an interpretation as
probabilistic correlations in loop $O(n)$ models, they are always positive when
$\kappa\in (8/3,8)$, while they may have zeroes for $\kappa\leq 8/3$. They also
admit a Fr\"{o}benius series expansion that matches with the algebraic content
from CFT. Moreover, we check that at the first level of fusion, they have
logarithmic asymptotic behavior when $\kappa=8/3$ and $\kappa=8$, in accordance
with logarithmic minimal models $M(2,1)$ and $M(2,3)$, respectively.
  Second, we construct SLE${}_\kappa$ pure partition functions and show that
they are continuous in $\kappa\in (0,8)$ and they decay to zero as a polynomial
of $(8-\kappa)$ when $\kappa\to 8$. We explicitly relate the Coulomb gas
integrals and pure partition functions together in terms of the meander matrix.
As a by-product, our results yield a construction of global non-simple multiple
chordal SLE${}_\kappa$ measures ($\kappa \in (4,8)$) uniquely determined by
their re-sampling property.
