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

Abstract

We study the quantum structure of four-dimensional {{mathcal {N}}}=2 superfield sigma-model formulated in harmonic superspace in terms of the omega-hypermultiplet superfield omega . The model is described by harmonic superfield sigma-model metric g_{ab}(omega ) and two potential-like superfields L^{++}_{a}(omega ) and L^{(+4)}(omega ). In bosonic component sector this model describes some hyper-Kähler manifold. The manifestly {{mathcal {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}(omega ), L^{++}_{a}(omega ), L^{(+4)}(omega ), where some specific analogy between the algebra of covariant derivatives in the sigma-model and the corresponding algebra in the {{mathcal {N}}}=2 SYM theory is used. The component structure of divergences in the bosonic sector is discussed.