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Induced low-energy effective action in the 6D, N=(1,0) hypermultiplet theory on the vector multiplet background

We consider the six dimensional N=(1,0) hypermultiplet model coupled to an external field of the Abelian vector multiplet in harmonic superspace approach. Using the superfield proper-time technique we find the divergent part of the effective action and derive the complete finite induced low-energy superfield effective action. This effective action depends on external field and contains in bosonic sector all the powers of the constant Maxwell field strength. The obtained result can be treated as the 6D, N=(1,0) supersymmetric Heisenberg-Euler type effective action.