Abstract
The exact expressions for integrated maximal U(1)Y violating (MUV) n-point correlators in SU(N) mathcal{N} = 4 supersymmetric Yang-Mills theory are determined. The analysis generalises previous results on the integrated correlator of four superconformal primaries and is based on supersymmetric localisation. The integrated correlators are functions of N and τ = θ/(2π) + 4πi/ {g}_{YM}^2 , and are expressed as two-dimensional lattice sums that are modular forms with holomorphic and anti-holomorphic weights (w, −w) where w = n − 4. The correlators satisfy Laplace-difference equations that relate the SU(N+1), SU(N) and SU(N−1) expressions and generalise the equations previously found in the w = 0 case. The correlators can be expressed as infinite sums of Eisenstein modular forms of weight (w, −w). For any fixed value of N the perturbation expansion of this correlator is found to start at order ( {g}_{YM}^2 N)w. The contributions of Yang-Mills instantons of charge k > 0 are of the form qkf(gYM), where q = e2πiτ and f(gYM) = O( {g}_{YM}^{-2w} ) when {g}_{YM}^2 ≪ 1. Anti-instanton contributions have charge k < 0 and are of the form {overline{q}}^{left|kright|}hat{f}left({g}_{YM}right) , where hat{f}left({g}_{YM}right)=Oleft({g}_{YM}^{2w}right) when {g}_{YM}^2 ≪ 1. Properties of the large-N expansion are in agreement with expectations based on the low energy expansion of flat-space type IIB superstring amplitudes. We also comment on the identification of n-point free-field MUV correlators with the integrands of (n − 4)-loop perturbative contributions to the four-point correlator. In particular, we emphasise the important rôle of SL(2, ℤ)-covariance in the construction.
Highlights
Supersymmetric SU(N ) Yang-Mills (SYM) theory can be determined by supersymmetric localisation in the manner described in [3] and briefly reviewed in appendix A
The parameter m is the mass of the hypermultiplet and in the limit m = 0 the N = 2 supersymmetry is extended to N = 4
In the earlier papers, which were based on the application of supersymmetric localisation techniques [4] to the integrated four-point function described in [3], the integrated correlator GN (τ, τ) was recast as a two-dimensional lattice sum, which made its modular properties manifest and from which it was simple to analyse its dependence on N and the coupling constant, τ
Summary
This lattice sum can be expressed as an infinite sum of Eisenstein modular forms (which are defined and summarised in appendix B). Π2, while for λ 1 perturbation theory produces an asymptotic, factorially growing, divergent series This strong coupling seri√es is not Borel summable and its non-perturbative completion, which behaves as O(λw/2e−2 λ), is determined using resurgence techniques.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
