On a structure of the one-loop divergences in 4 D 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.