F-polynomials are certain polynomials appears in the expansion formula of a cluster variable, see for example the formula (6.5) in cluster algebras IV. Theta functions in the paper correspond to cluster variables. Are there some relations between F-polynomials and theta functions? Thank you very much.

The cluster variables are a subset of the $\Theta$ variables. (More generally, the cluster monomials are a subset of the $\Theta$ variables. By definition, a cluster monomial is a monomial of the form $\prod_{i=1}^n x_i^{a_i}$ where $(x_1, \ldots, x_n)$ is a cluster and the $a_i$ are $\geq 0$.) The $F$-polynomials are related to the $\Theta$ variables by a simple change of variable described in Cluster Algebras IV.