  Strongly interacting massive particles are viable dark matter candidates. We
consider a dark $Sp(4)$ gauge theory with $N_f=2$ fermions in the pseudo-real
fundamental representation and construct the chiral low-energy effective
theory. We determine the flavor multiplet structure and the chiral Lagrangian,
including the Wess-Zumino-Witten term for mass-degenerate and non-degenerate
flavors. We then study the possible charge assignments under a $U(1)'$ gauge
symmetry, emphasizing on dark state stability, and provide the full Lagrangian
description for Goldstone bosons and vector resonances, including the
Wess-Zumino-Witten term. Finally, we use dedicated lattice simulations to
determine the chiral low-energy effective theory's validity and low-energy
constants. This work represents a self-consistent study of this non-Abelian
theory. It thereby provides a framework for future phenomenological exploration
in connection to the dark matter problem.
