Mayer expansion of the Nekrasov pre potential: the subleading ${\epsilon }_2$-order

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 ${\epsilon }_2$-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.

29 pages, 9 figures

References in corpus (13)

• Gluon scattering amplitudes at strong coupling
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• Deforming SW curve
• Gauge theories on Omega-backgrounds from non commutative Seiberg-Witten curves
• Cohomological gauge theory, quiver matrix models and Donaldson-Thomas theory
• Nekrasov prepotential with fundamental matter from the quantum spin chain
• Asymptotic Bethe Ansatz on the GKP vacuum as a defect spin chain: scattering, particles and minimal area Wilson loops
• Yangian associated with 2D $\mathcal{N}=1$ SCFT
• Spherical Hecke algebra in the Nekrasov-Shatashvili limit
• Finite ${\epsilon }_2$-corrections to the $\mathcal{N}=2$ SYM prepotential
• N=2 gauge theories, instanton moduli spaces and geometric representation theory

Cited by in corpus (9)

• A slow review of the AGT correspondence
• Holomorphic field realization of SH${}^c$ and quantum geometry of quiver gauge theories
• A note on the algebraic engineering of 4D $\mathcal{N}=2$ super Yang-Mills theories
• Fermions and scalars in $\mathcal{N}=4$ Wilson loops at strong coupling and beyond
• Strong Wilson polygons from the lodge of free and bound mesons
• The contribution of scalars to $\mathcal{N}=4$ SYM amplitudes II: Young tableaux, asymptotic factorisation and strong coupling
• Quantum integrability of $\mathcal{N}=2$ 4d gauge theories
• Seiberg-Witten period relations in Omega background
• A Young diagram expansion of the hexagonal Wilson loop (amplitude) in $\mathcal{N}=4$ SYM