Finite ${\epsilon }_2$-corrections to the $\mathcal{N}=2$ SYM prepotential

Abstract

We derive the first ${\epsilon }_2$-correction to the instanton partition functions of $\mathcal{N}=2$ Super Yang-Mills (SYM) in four dimensions in the Nekrasov-Shatashvili limit ${\epsilon }_2\to 0$. In the latter we recall the emergence of the famous Thermodynamic Bethe Ansatz-like equation which has been found by Mayer expansion techniques. Here we combine efficiently these to field theory arguments. In a nutshell, we find natural and resolutive the introduction of a new operator $\nabla$ that distinguishes the singularities within and outside the integration contour of the partition function.

13 pages, 1 figure

References in corpus (14)

• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• Seiberg-Witten Theory and Random Partitions
• Deforming SW curve
• Gauge theories on Omega-backgrounds from non commutative Seiberg-Witten curves
• 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
• Classical irregular block, N=2 pure gauge theory and Mathieu equation
• General instanton counting and 5d SCFT
• Classical Virasoro irregular conformal block
• On the Jeffrey-Kirwan residue of BCD-instantons
• Semi-classical analysis of the inner product of Bethe states
• Classical Virasoro irregular conformal block II
• Spherical Hecke algebra in the Nekrasov-Shatashvili limit
• Recursive Method for Nekrasov partition function for classical Lie groups

Cited by in corpus (13)

• Hexagonal Wilson Loops in Planar $\mathcal{N}=4$ SYM Theory at Finite Coupling
• 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
• On the scattering of gluons in the GKP string
• 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
• Mayer expansion of the Nekrasov pre potential: the subleading ${\epsilon }_2$-order
• Quantum integrability of $\mathcal{N}=2$ 4d gauge theories
• Seiberg-Witten period relations in Omega background
• $\mathcal{N}=4$ polygonal Wilson loops: fermions
• A Young diagram expansion of the hexagonal Wilson loop (amplitude) in $\mathcal{N}=4$ SYM