We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.

Durham Research Online
You are in:

Exact expressions for n-point maximal U(1)_Y-violating integrated correlators in SU(N)\mathcal{N}=4 SYM

Dorigoni, Daniele and Green, Michael B. and Wen, Congkao (2021) 'Exact expressions for n-point maximal U(1)_Y-violating integrated correlators in SU(N)\mathcal{N}=4 SYM.', Journal of high energy physics., 2021 . p. 132.


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 τ = θ/(2π) + 4πi/g2 Y M , 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 2 Y M N) w. The contributions of Yang–Mills instantons of charge k > 0 are of the form q k f(gY M ), where q = e 2πiτ and f(gY M ) = O(g −2w Y M ) when g 2 Y M 1. Anti-instanton contributions have charge k < 0 and are of the form ¯q |k| ˆf(gY M ), where ˆf(gY M ) = O(g 2w Y M ) when g 2 Y M 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 rˆole of SL(2, Z)-covariance in the construction.

Item Type:Article
Full text:Publisher-imposed embargo
(AM) Accepted Manuscript
Available under License - Creative Commons Attribution 4.0.
File format - PDF
Full text:(VoR) Version of Record
Available under License - Creative Commons Attribution 4.0.
Download PDF
Publisher Web site:
Publisher statement:Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Date accepted:23 October 2021
Date deposited:13 October 2021
Date of first online publication:18 November 2021
Date first made open access:25 January 2022

Save or Share this output

Look up in GoogleScholar