dc.contributor.author | Dorigoni, D | |
dc.contributor.author | Green, MB | |
dc.contributor.author | Wen, C | |
dc.date.accessioned | 2021-06-16T10:17:15Z | |
dc.date.available | 2021-06-16T10:17:15Z | |
dc.date.issued | 2021-05-12 | |
dc.identifier.citation | Dorigoni, Daniele et al. "Exact Properties Of An Integrated Correlator In $$ \Mathcal{N} $$ = 4 SU(N) SYM". Journal Of High Energy Physics, vol 2021, no. 5, 2021. Springer Science And Business Media LLC, doi:10.1007/jhep05(2021)089. Accessed 16 June 2021. | en_US |
dc.identifier.issn | 1126-6708 | |
dc.identifier.uri | https://qmro.qmul.ac.uk/xmlui/handle/123456789/72566 | |
dc.description.abstract | We present a novel expression for an integrated correlation function of four superconformal primaries in SU(N) N = 4 supersymmetric Yang-Mills (N = 4 SYM) theory. This integrated correlator, which is based on supersymmetric localisation, has been the subject of several recent developments. In this paper the correlator is re-expressed as a sum over a two dimensional lattice that is valid for all N and all values of the complex Yang-Mills coupling τ=θ/2π+4πi/g2YM. In this form it is manifestly invariant under SL(2, ℤ) Montonen-Olive duality. Furthermore, it satisfies a remarkable Laplace-difference equation that relates the SU(N) correlator to the SU(N + 1) and SU(N − 1) correlators. For any fixed value of N the correlator can be expressed as an infinite series of non-holomorphic Eisenstein series, E(s;τ,τ¯¯¯) with s ∈ ℤ, and rational coefficients that depend on the values of N and s. The perturbative expansion of the integrated correlator is an asymptotic but Borel summable series, in which the n-loop coefficient of order (gYM/π)2n is a rational multiple of ζ(2n + 1). The n = 1 and n = 2 terms agree precisely with results determined directly by integrating the expressions in one-loop and two-loop perturbative N = 4 SYM field theory. Likewise, the charge-k instanton contributions (|k| = 1, 2, . . .) have an asymptotic, but Borel summable, series of perturbative corrections. The large-N expansion of the correlator with fixed τ is a series in powers of N12−ℓ (ℓ ∈ ℤ) with coefficients that are rational sums of E(s;τ,τ¯¯¯) with s ∈ ℤ + 1/2. This gives an all orders derivation of the form of the recently conjectured expansion. We further consider the ’t Hooft topological expansion of large-N Yang-Mills theory in which λ=g2YMN is fixed. The coefficient of each order in the 1/N expansion can be expanded as a series of powers of λ that converges for |λ| < π2. For large λ this becomes an asymptotic series when expanded in powers of 1/λ−−√ with coefficients that are again rational multiples of odd zeta values, in agreement with earlier results and providing new ones. We demonstrate that the large-λ series is not Borel summable, and determine its resurgent non-perturbative completion, which is O(exp(−2λ−−√)). | en_US |
dc.format.extent | 89 - ? | |
dc.publisher | Springer | en_US |
dc.relation.ispartof | Journal of High Energy Physics | |
dc.rights | 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. | |
dc.rights | Attribution 3.0 United States | * |
dc.rights.uri | http://creativecommons.org/licenses/by/3.0/us/ | * |
dc.title | Exact properties of an integrated correlator in N = 4 SU(N) SYM | en_US |
dc.type | Article | en_US |
dc.rights.holder | © 2021, The Author(s) | |
dc.identifier.doi | 10.1007/jhep05(2021)089 | |
pubs.issue | 5 | en_US |
pubs.notes | Not known | en_US |
pubs.volume | 2021 | en_US |
rioxxterms.funder | Default funder | en_US |
rioxxterms.identifier.project | Default project | en_US |
qmul.funder | Royal Society University Research Fellowship::Royal Society | en_US |