On a structure of the one-loop divergences in 4D harmonic superspace sigma-model

We study the quantum structure of four-dimensional N = 2 superfield sigma-model formulated in harmonic superspace in terms of the omega-hypermultiplet superfield ω. The model is described by harmonic superfield sigma-model metric g${}_{ab}$(ω) and two potential-like superfields L${}_a^{++}$(ω) and L${}^{(+4)}$(ω). In bosonic component sector this model describes some hyper-Kähler manifold. The manifestly N = 2 supersymmetric covariant background-quantum splitting is constructed and the superfield proper-time technique is developed to calculate the one-loop effective action. The one-loop divergences of the superfield effective action are found for arbitrary g${}_{ab}$(ω), L${}_a^{++}$(ω), L${}^{(+4)}$(ω), where some specific analogy between the algebra of covariant derivatives in the sigma-model and the corresponding algebra in the N = 2 SYM theory is used. The component structure of divergences in the bosonic sector is discussed.