Exceptionally simple integrated correlators in N $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills theory
Abstract Supersymmetric localisation has led to several modern developments in the study of integrated correlators in N $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills (SYM) theory. In particular, exact results have been derived for certain integrated four-point functions of superconformal primary o...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-09-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP09(2023)203 |
| _version_ | 1797371223603150848 |
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| author | Daniele Dorigoni Paolo Vallarino |
| author_facet | Daniele Dorigoni Paolo Vallarino |
| author_sort | Daniele Dorigoni |
| collection | DOAJ |
| description | Abstract Supersymmetric localisation has led to several modern developments in the study of integrated correlators in N $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills (SYM) theory. In particular, exact results have been derived for certain integrated four-point functions of superconformal primary operators in the stress tensor multiplet which are valid for all classical gauge groups, SU(N), SO(N), and USp(2N), and for all values of the complex coupling, τ = θ/(2π) + 4πi/ g YM 2 $$ {g}_{YM}^2 $$ . In this work we extend this analysis and provide a unified two-dimensional lattice sum representation valid for all simple gauge groups, in particular for the exceptional series E r (with r = 6, 7, 8), F 4 and G 2. These expressions are manifestly covariant under Goddard-Nuyts-Olive duality which for the cases of F 4 and G 2 is given by particular Fuchsian groups. We show that the perturbation expansion of these integrated correlators is universal in the sense that it can be written as a single function of three parameters, called Vogel parameters, and a suitable ’t Hooft-like coupling. To obtain the perturbative expansion for the integrated correlator with a given gauge group we simply need substituting in this single universal expression specific values for the Vogel parameters. At the non-perturbative level we conjecture a formula for the one-instanton Nekrasov partition function valid for all simple gauge groups and for general Ω-deformation background. We check that our expression reduces in various limits to known results and that it produces, via supersymmetric localisation, the same one-instanton contribution to the integrated correlator as the one derived from the lattice sum representation. Finally, we consider the action of the hyperbolic Laplace operator with respect to τ on the integrated correlators with exceptional gauge groups and derive inhomogeneous Laplace equations very similar to the ones previously obtained for classical gauge groups. |
| first_indexed | 2024-03-08T18:15:45Z |
| format | Article |
| id | doaj.art-95c12e6c72894909a9eeac1b7be270c2 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-08T18:15:45Z |
| publishDate | 2023-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-95c12e6c72894909a9eeac1b7be270c22023-12-31T12:08:56ZengSpringerOpenJournal of High Energy Physics1029-84792023-09-012023914110.1007/JHEP09(2023)203Exceptionally simple integrated correlators in N $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills theoryDaniele Dorigoni0Paolo Vallarino1Centre for Particle Theory & Department of Mathematical Sciences, Durham UniversityUniversità di Torino, Dipartimento di Fisica and I.N.F.N. - sezione di TorinoAbstract Supersymmetric localisation has led to several modern developments in the study of integrated correlators in N $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills (SYM) theory. In particular, exact results have been derived for certain integrated four-point functions of superconformal primary operators in the stress tensor multiplet which are valid for all classical gauge groups, SU(N), SO(N), and USp(2N), and for all values of the complex coupling, τ = θ/(2π) + 4πi/ g YM 2 $$ {g}_{YM}^2 $$ . In this work we extend this analysis and provide a unified two-dimensional lattice sum representation valid for all simple gauge groups, in particular for the exceptional series E r (with r = 6, 7, 8), F 4 and G 2. These expressions are manifestly covariant under Goddard-Nuyts-Olive duality which for the cases of F 4 and G 2 is given by particular Fuchsian groups. We show that the perturbation expansion of these integrated correlators is universal in the sense that it can be written as a single function of three parameters, called Vogel parameters, and a suitable ’t Hooft-like coupling. To obtain the perturbative expansion for the integrated correlator with a given gauge group we simply need substituting in this single universal expression specific values for the Vogel parameters. At the non-perturbative level we conjecture a formula for the one-instanton Nekrasov partition function valid for all simple gauge groups and for general Ω-deformation background. We check that our expression reduces in various limits to known results and that it produces, via supersymmetric localisation, the same one-instanton contribution to the integrated correlator as the one derived from the lattice sum representation. Finally, we consider the action of the hyperbolic Laplace operator with respect to τ on the integrated correlators with exceptional gauge groups and derive inhomogeneous Laplace equations very similar to the ones previously obtained for classical gauge groups.https://doi.org/10.1007/JHEP09(2023)203Duality in Gauge Field TheoriesNonperturbative EffectsSupersymmetric Gauge Theory |
| spellingShingle | Daniele Dorigoni Paolo Vallarino Exceptionally simple integrated correlators in N $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills theory Journal of High Energy Physics Duality in Gauge Field Theories Nonperturbative Effects Supersymmetric Gauge Theory |
| title | Exceptionally simple integrated correlators in N $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills theory |
| title_full | Exceptionally simple integrated correlators in N $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills theory |
| title_fullStr | Exceptionally simple integrated correlators in N $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills theory |
| title_full_unstemmed | Exceptionally simple integrated correlators in N $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills theory |
| title_short | Exceptionally simple integrated correlators in N $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills theory |
| title_sort | exceptionally simple integrated correlators in n mathcal n 4 supersymmetric yang mills theory |
| topic | Duality in Gauge Field Theories Nonperturbative Effects Supersymmetric Gauge Theory |
| url | https://doi.org/10.1007/JHEP09(2023)203 |
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