Abstract
We consider two-point correlators in SU(N) gauge theories on R4 with N=2 supersymmetry and Nf massless hypermultiplets in the fundamental representation. Using localization on S4, we compute the leading perturbative corrections to the two-point functions of chiral/anti-chiral operators made of scalar fields. The results are compared at two and three loops against direct field theory computations for some special operators whose correlators remain finite in perturbation theory at the specific loop order. In the conformal case, the match is shown up to two loops for a generic choice of operators and for arbitrary N.
Highlights
Non-perturbative effects in gauge theories with N = 2 supersymmetry in four dimensions can be computed in many different ways
The partition function ZS4 is at the core of this paper, in which we want to test the predictions of localization against the results obtained by computing the Feynman diagrams in standard perturbation theory
The localization formula reduces to a Gaussian matrix model integral counting the number of ladder diagrams, in full agreement with the field theory predictions [8]
Summary
Perturbative tests of the localization formulae have already been performed for Wilson loops in N = 4 theories for which both one-loop and instanton corrections to the gauge partition function are absent In this case, the localization formula reduces to a Gaussian matrix model integral counting the number of ladder diagrams, in full agreement with the field theory predictions [8]. Given that the correspondence directly works at the level of diagrams, it is natural to ask whether and to what extent it can be extended to non-conformal N = 2 SYM theories, such as theories with gauge group SU(N ) and Nf = 2N massless hypermultiplets in the fundamental representation In this case the sphere partition function can still be computed using localization in terms of a matrix model whose structure is similar to the one of conformal cases.
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