Mayer expansion of the Nekrasov prepotential: The subleading ε2-order

The Mayer cluster expansion technique is applied to the Nekrasov instanton partition function of N=2N=2SU(Nc)SU(Nc) super Yang–Mills. The subleading small ε2ε2-correction to the Nekrasov–Shatashvili limiting value of the prepotential is determined by a detailed analysis of all the one-loop diagrams. Indeed, several types of contributions can be distinguished according to their origin: long range interaction or potential expansion, clusters self-energy, internal structure, one-loop cyclic diagrams, etc. The field theory result derived more efficiently in [1], under some minor technical assumptions, receives here definite confirmation thanks to several remarkable cancellations: in this way, we may infer the validity of these assumptions for further computations in the field theoretical approach.