Abstract
We derive the first ε2-correction of the instanton partition functions in 4D N=2 Super Yang–Mills (SYM) to the Nekrasov–Shatashvili limit ε2→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 ∇ that distinguishes the singularities within and outside the integration contour of the partition function.
Highlights
The Omega background was first introduced in N = 2 SUSY gauge theories to regularise the infinite volume of R4 in the computation of instanton contributions to the partition function by localisation [1]
It has proven to be a formidable way to preserve integrability of these theories upon deformation. This background is characterised by two equivariant deformation parameters ε1 and ε2 associated to the breaking of the Lorentz invariant four dimensional space into C × C, but still the Nekrasov instanton partition function exhibits an integrable structure in the form of covariance under the Spherical Hecke central (SHc) algebra [2, 3]
We have further computed the irreducible clusters with four vertices for a potential corresponding to U (1) Super Yang-Mills (SYM) and we have found the same conclusion
Summary
It has proven to be a formidable way to preserve integrability of these theories upon deformation This background is characterised by two equivariant deformation parameters ε1 and ε2 associated to the breaking of the Lorentz invariant four dimensional space into C × C, but still the Nekrasov instanton partition function exhibits an integrable structure in the form of covariance under the Spherical Hecke central (SHc) algebra [2, 3] (which is formally equivalent to a W∞ algebra). A more detailed computation involving only the combinatorics of the Mayer expansion is to appear shortly [24]
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