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arXiv · 1511.02672

Mayer expansion of the Nekrasov pre potential: the subleading $ε_2$-order

Jean-Emile Bourgine·Davide Fioravanti
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Abstract

The Mayer cluster expansion technique is applied to the Nekrasov instanton partition function of $\mathcal{N}=2$ $SU(N_c)$ super Yang-Mills. The subleading small $ε_2$-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.

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Jean-Emile Bourgine, Davide Fioravanti. 2015-11-09. Mayer expansion of the Nekrasov pre potential: the subleading $ε_2$-order. https://doi.org/10.1016/j.nuclphysb.2016.03.017

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