Far beyond the planar limit in strongly-coupled N $$ \mathcal{N} $$ = 4 SYM
Abstract When the SU(N) N $$ \mathcal{N} $$ = 4 super-Yang-Mills (SYM) theory with complexified gauge coupling τ is placed on a round four-sphere and deformed by an N $$ \mathcal{N} $$ = 2-preserving mass parameter m, its free energy F (m, τ, τ ¯ $$ \overline{\tau} $$ ) can be computed exactly using...
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doaj-1bd0e57e575b4071b3c217049382c76c2021-01-24T12:06:37ZengSpringerOpenJournal of High Energy Physics1029-84792021-01-012021113710.1007/JHEP01(2021)103Far beyond the planar limit in strongly-coupled N $$ \mathcal{N} $$ = 4 SYMShai M. Chester0Silviu S. Pufu1Department of Particle Physics and Astrophysics, Weizmann Institute of ScienceJoseph Henry Laboratories, Princeton UniversityAbstract When the SU(N) N $$ \mathcal{N} $$ = 4 super-Yang-Mills (SYM) theory with complexified gauge coupling τ is placed on a round four-sphere and deformed by an N $$ \mathcal{N} $$ = 2-preserving mass parameter m, its free energy F (m, τ, τ ¯ $$ \overline{\tau} $$ ) can be computed exactly using supersymmetric localization. In this work, we derive a new exact relation between the fourth derivative ∂ m 4 F m τ τ ¯ m = 0 $$ {\partial}_m^4F\left(m,\tau, \overline{\tau}\right)\left|{{}_m}_{=0}\right. $$ of the sphere free energy and the integrated stress-tensor multiplet four-point function in the N $$ \mathcal{N} $$ = 4 SYM theory. We then apply this exact relation, along with various other constraints derived in previous work (coming from analytic bootstrap, the mixed derivative ∂ τ ∂ τ ¯ ∂ m 2 F m τ τ ¯ m = 0 $$ {\partial}_{\tau }{\partial}_{\overline{\tau}}{\partial}_m^2F\left(m,\tau, \overline{\tau}\right)\left|{{}_m}_{=0}\right. $$ , and type IIB superstring theory scattering amplitudes) to determine various perturbative terms in the large N and large ’t Hooft coupling λ expansion of the N $$ \mathcal{N} $$ = 4 SYM correlator at separated points. In particular, we determine the leading large-λ term in the N $$ \mathcal{N} $$ = 4 SYM correlation function at order 1/N 8. This is three orders beyond the planar limit.https://doi.org/10.1007/JHEP01(2021)1031/N ExpansionAdS-CFT CorrespondenceExtended Supersymmetry |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Shai M. Chester Silviu S. Pufu |
spellingShingle |
Shai M. Chester Silviu S. Pufu Far beyond the planar limit in strongly-coupled N $$ \mathcal{N} $$ = 4 SYM Journal of High Energy Physics 1/N Expansion AdS-CFT Correspondence Extended Supersymmetry |
author_facet |
Shai M. Chester Silviu S. Pufu |
author_sort |
Shai M. Chester |
title |
Far beyond the planar limit in strongly-coupled N $$ \mathcal{N} $$ = 4 SYM |
title_short |
Far beyond the planar limit in strongly-coupled N $$ \mathcal{N} $$ = 4 SYM |
title_full |
Far beyond the planar limit in strongly-coupled N $$ \mathcal{N} $$ = 4 SYM |
title_fullStr |
Far beyond the planar limit in strongly-coupled N $$ \mathcal{N} $$ = 4 SYM |
title_full_unstemmed |
Far beyond the planar limit in strongly-coupled N $$ \mathcal{N} $$ = 4 SYM |
title_sort |
far beyond the planar limit in strongly-coupled n $$ \mathcal{n} $$ = 4 sym |
publisher |
SpringerOpen |
series |
Journal of High Energy Physics |
issn |
1029-8479 |
publishDate |
2021-01-01 |
description |
Abstract When the SU(N) N $$ \mathcal{N} $$ = 4 super-Yang-Mills (SYM) theory with complexified gauge coupling τ is placed on a round four-sphere and deformed by an N $$ \mathcal{N} $$ = 2-preserving mass parameter m, its free energy F (m, τ, τ ¯ $$ \overline{\tau} $$ ) can be computed exactly using supersymmetric localization. In this work, we derive a new exact relation between the fourth derivative ∂ m 4 F m τ τ ¯ m = 0 $$ {\partial}_m^4F\left(m,\tau, \overline{\tau}\right)\left|{{}_m}_{=0}\right. $$ of the sphere free energy and the integrated stress-tensor multiplet four-point function in the N $$ \mathcal{N} $$ = 4 SYM theory. We then apply this exact relation, along with various other constraints derived in previous work (coming from analytic bootstrap, the mixed derivative ∂ τ ∂ τ ¯ ∂ m 2 F m τ τ ¯ m = 0 $$ {\partial}_{\tau }{\partial}_{\overline{\tau}}{\partial}_m^2F\left(m,\tau, \overline{\tau}\right)\left|{{}_m}_{=0}\right. $$ , and type IIB superstring theory scattering amplitudes) to determine various perturbative terms in the large N and large ’t Hooft coupling λ expansion of the N $$ \mathcal{N} $$ = 4 SYM correlator at separated points. In particular, we determine the leading large-λ term in the N $$ \mathcal{N} $$ = 4 SYM correlation function at order 1/N 8. This is three orders beyond the planar limit. |
topic |
1/N Expansion AdS-CFT Correspondence Extended Supersymmetry |
url |
https://doi.org/10.1007/JHEP01(2021)103 |
work_keys_str_mv |
AT shaimchester farbeyondtheplanarlimitinstronglycouplednmathcaln4sym AT silviuspufu farbeyondtheplanarlimitinstronglycouplednmathcaln4sym |
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1724326349785530368 |