Exact expressions for n-point maximal U(1)Y-violating integrated correlators in SU(N) N=4 SYM

The exact expressions for integrated maximal U(1)(Y) violating (MUV) n-point correlators in SU(N) 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 tau = theta/(2 pi) + 4 pi i/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 q(k) f (g(YM)), where q = e(2 pi i tau) and f (g(YM)) = O(g(YM)(-2w)) when g(YM)(2 )<< 1. Anti-instanton contributions have charge k < 0 and are of the form q(-vertical bar k vertical bar)(f) over cap (g(YM)), where (f) over cap (g(YM)) = O(g(YM)(2w)) 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 role of SL(2, Z)-covariance in the construction.

Automated summary

The exact expressions for integrated maximal U(1)(Y) violating (MUV) n-point correlators in SU(N) N = 4 supersymmetric Yang-Mills theory have been determined using supersymmetric localisation. These integrated correlators satisfy Laplace-difference equations and can be expressed as infinite sums of Eisenstein modular forms.