  We study the spectral function of a single hole doped into the (a,b) plane of
the Mott insulator LaVO$_3$, with antiferromagnetic (AF) spin order of S=1
spins accompanied by alternating orbital (AO) order of active
$\{d_{yz},d_{zx}\}$ orbitals. Starting from the respective t-J model, with
spin-orbital superexchange and effective three-site hopping terms, we derive
the polaron Hamiltonian and show that a hole couples simultaneously to the
collective excitations of the AF/AO phase, magnons and orbitons. Next, we solve
this polaron problem using the self-consistent Born approximation and find a
stable quasiparticle solution -- a spin-orbital polaron. We show that the
spin-orbital polaron resembles the orbital polaron found in $e_g$ systems, as
e.g. in K$_2$CuF$_4$ or (to some extent) in LaMnO$_3$, and that the hole may be
seen as confined in a string-like potential. However, the spins also play a
crucial role in the formation of this polaron -- we explain how the orbital
degrees of freedom: (i) confine the spin dynamics acting on the hole as the
classical Ising spins, and (ii) generate the string potential which is of the
joint spin-orbital character. Finally, we discuss the impact of the results
presented here on the understanding of the phase diagrams of the lightly doped
cubic vanadates.
