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

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

Abstract The exact expressions for integrated maximal U(1) Y violating (MUV) n-point correlators in SU(N) 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 s...

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Autores principales: Daniele Dorigoni, Michael B. Green, Congkao Wen
Formato: article
Lenguaje:EN
Publicado: SpringerOpen 2021
Materias:
Conformal Field Theory
Nonperturbative Effects
Scattering Amplitudes
Supersymmetry and Duality
Nuclear and particle physics. Atomic energy. Radioactivity
QC770-798
Acceso en línea:https://doaj.org/article/8f19faf2e77d4171a00688f7e2693fce
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spelling oai:doaj.org-article:8f19faf2e77d4171a00688f7e2693fce2021-11-21T12:41:16ZExact expressions for n-point maximal U(1) Y -violating integrated correlators in SU(N) N $$ \mathcal{N} $$ = 4 SYM10.1007/JHEP11(2021)1321029-8479https://doaj.org/article/8f19faf2e77d4171a00688f7e2693fce2021-11-01T00:00:00Zhttps://doi.org/10.1007/JHEP11(2021)132https://doaj.org/toc/1029-8479Abstract The exact expressions for integrated maximal U(1) Y violating (MUV) n-point correlators in SU(N) 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 $$ {g}_{YM}^2 $$ , 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 $$ {g}_{YM}^2 $$ N) w . The contributions of Yang-Mills instantons of charge k > 0 are of the form q k f(g YM ), where q = e 2πiτ and f(g YM ) = O( g YM − 2 w $$ {g}_{YM}^{-2w} $$ ) when g YM 2 $$ {g}_{YM}^2 $$ ≪ 1. Anti-instanton contributions have charge k < 0 and are of the form q ¯ k f ̂ g YM $$ {\overline{q}}^{\left|k\right|}\hat{f}\left({g}_{YM}\right) $$ , where f ̂ g YM = O g YM 2 w $$ \hat{f}\left({g}_{YM}\right)=O\left({g}_{YM}^{2w}\right) $$ when g YM 2 $$ {g}_{YM}^2 $$ ≪ 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.Daniele DorigoniMichael B. GreenCongkao WenSpringerOpenarticleConformal Field TheoryNonperturbative EffectsScattering AmplitudesSupersymmetry and DualityNuclear and particle physics. Atomic energy. RadioactivityQC770-798ENJournal of High Energy Physics, Vol 2021, Iss 11, Pp 1-36 (2021)
institution DOAJ
collection DOAJ
language EN
topic Conformal Field Theory
Nonperturbative Effects
Scattering Amplitudes
Supersymmetry and Duality
Nuclear and particle physics. Atomic energy. Radioactivity
QC770-798
spellingShingle Conformal Field Theory
Nonperturbative Effects
Scattering Amplitudes
Supersymmetry and Duality
Nuclear and particle physics. Atomic energy. Radioactivity
QC770-798
Daniele Dorigoni
Michael B. Green
Congkao Wen
Exact expressions for n-point maximal U(1) Y -violating integrated correlators in SU(N) N $$ \mathcal{N} $$ = 4 SYM
description Abstract The exact expressions for integrated maximal U(1) Y violating (MUV) n-point correlators in SU(N) 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 $$ {g}_{YM}^2 $$ , 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 $$ {g}_{YM}^2 $$ N) w . The contributions of Yang-Mills instantons of charge k > 0 are of the form q k f(g YM ), where q = e 2πiτ and f(g YM ) = O( g YM − 2 w $$ {g}_{YM}^{-2w} $$ ) when g YM 2 $$ {g}_{YM}^2 $$ ≪ 1. Anti-instanton contributions have charge k < 0 and are of the form q ¯ k f ̂ g YM $$ {\overline{q}}^{\left|k\right|}\hat{f}\left({g}_{YM}\right) $$ , where f ̂ g YM = O g YM 2 w $$ \hat{f}\left({g}_{YM}\right)=O\left({g}_{YM}^{2w}\right) $$ when g YM 2 $$ {g}_{YM}^2 $$ ≪ 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.
format article
author Daniele Dorigoni
Michael B. Green
Congkao Wen
author_facet Daniele Dorigoni
Michael B. Green
Congkao Wen
author_sort Daniele Dorigoni
title Exact expressions for n-point maximal U(1) Y -violating integrated correlators in SU(N) N $$ \mathcal{N} $$ = 4 SYM
title_short Exact expressions for n-point maximal U(1) Y -violating integrated correlators in SU(N) N $$ \mathcal{N} $$ = 4 SYM
title_full Exact expressions for n-point maximal U(1) Y -violating integrated correlators in SU(N) N $$ \mathcal{N} $$ = 4 SYM
title_fullStr Exact expressions for n-point maximal U(1) Y -violating integrated correlators in SU(N) N $$ \mathcal{N} $$ = 4 SYM
title_full_unstemmed Exact expressions for n-point maximal U(1) Y -violating integrated correlators in SU(N) N $$ \mathcal{N} $$ = 4 SYM
title_sort exact expressions for n-point maximal u(1) y -violating integrated correlators in su(n) n $$ \mathcal{n} $$ = 4 sym
publisher SpringerOpen
publishDate 2021
url https://doaj.org/article/8f19faf2e77d4171a00688f7e2693fce
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AT michaelbgreen exactexpressionsfornpointmaximalu1yviolatingintegratedcorrelatorsinsunnmathcaln4sym
AT congkaowen exactexpressionsfornpointmaximalu1yviolatingintegratedcorrelatorsinsunnmathcaln4sym
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