Modular invariance in superstring theory from N $$ \mathcal{N} $$ = 4 super-Yang-Mills
Abstract We study the four-point function of the lowest-lying half-BPS operators in the N $$ \mathcal{N} $$ = 4 SU(N) super-Yang-Mills theory and its relation to the flat-space four-graviton amplitude in type IIB superstring theory. We work in a large-N expansion in which the complexified Yang-Mills...
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| Language: | English |
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SpringerOpen
2020-11-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | http://link.springer.com/article/10.1007/JHEP11(2020)016 |
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| author | Shai M. Chester Michael B. Green Silviu S. Pufu Yifan Wang Congkao Wen |
| author_facet | Shai M. Chester Michael B. Green Silviu S. Pufu Yifan Wang Congkao Wen |
| author_sort | Shai M. Chester |
| collection | DOAJ |
| description | Abstract We study the four-point function of the lowest-lying half-BPS operators in the N $$ \mathcal{N} $$ = 4 SU(N) super-Yang-Mills theory and its relation to the flat-space four-graviton amplitude in type IIB superstring theory. We work in a large-N expansion in which the complexified Yang-Mills coupling τ is fixed. In this expansion, non-perturbative instanton contributions are present, and the SL(2, ℤ) duality invariance of correlation functions is manifest. Our results are based on a detailed analysis of the sphere partition function of the mass-deformed SYM theory, which was previously computed using supersymmetric localization. This partition function determines a certain integrated correlator in the undeformed N $$ \mathcal{N} $$ = 4 SYM theory, which in turn constrains the four-point correlator at separated points. In a normalization where the two-point functions are proportional to N 2 − 1 and are independent of τ and τ ¯ $$ \overline{\tau} $$ , we find that the terms of order N $$ \sqrt{N} $$ and 1 / N $$ 1/\sqrt{N} $$ in the large N expansion of the four-point correlator are proportional to the non-holomorphic Eisenstein series E 3 2 τ τ ¯ $$ E\left(\frac{3}{2},\tau, \overline{\tau}\right) $$ and E 5 2 τ τ ¯ $$ E\left(\frac{5}{2},\tau, \overline{\tau}\right) $$ , respectively. In the flat space limit, these terms match the corresponding terms in the type IIB S-matrix arising from R 4 and D 4 R 4 contact inter-actions, which, for the R 4 case, represents a check of AdS/CFT at finite string coupling. Furthermore, we present striking evidence that these results generalize so that, at order N 1 2 − m $$ {N}^{\frac{1}{2}-m} $$ with integer m ≥ 0, the expansion of the integrated correlator we study is a linear sum of non-holomorphic Eisenstein series with half-integer index, which are manifestly SL(2, ℤ) invariant. |
| first_indexed | 2024-12-22T16:34:39Z |
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| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-22T16:34:39Z |
| publishDate | 2020-11-01 |
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| series | Journal of High Energy Physics |
| spelling | doaj.art-a317a2a8960544aab12d28f2b8fca7932022-12-21T18:19:59ZengSpringerOpenJournal of High Energy Physics1029-84792020-11-0120201115110.1007/JHEP11(2020)016Modular invariance in superstring theory from N $$ \mathcal{N} $$ = 4 super-Yang-MillsShai M. Chester0Michael B. Green1Silviu S. Pufu2Yifan Wang3Congkao Wen4Department of Particle Physics and Astrophysics, Weizmann Institute of ScienceSchool of Physics and Astronomy, Queen Mary University of LondonJoseph Henry Laboratories, Princeton UniversityJoseph Henry Laboratories, Princeton UniversitySchool of Physics and Astronomy, Queen Mary University of LondonAbstract We study the four-point function of the lowest-lying half-BPS operators in the N $$ \mathcal{N} $$ = 4 SU(N) super-Yang-Mills theory and its relation to the flat-space four-graviton amplitude in type IIB superstring theory. We work in a large-N expansion in which the complexified Yang-Mills coupling τ is fixed. In this expansion, non-perturbative instanton contributions are present, and the SL(2, ℤ) duality invariance of correlation functions is manifest. Our results are based on a detailed analysis of the sphere partition function of the mass-deformed SYM theory, which was previously computed using supersymmetric localization. This partition function determines a certain integrated correlator in the undeformed N $$ \mathcal{N} $$ = 4 SYM theory, which in turn constrains the four-point correlator at separated points. In a normalization where the two-point functions are proportional to N 2 − 1 and are independent of τ and τ ¯ $$ \overline{\tau} $$ , we find that the terms of order N $$ \sqrt{N} $$ and 1 / N $$ 1/\sqrt{N} $$ in the large N expansion of the four-point correlator are proportional to the non-holomorphic Eisenstein series E 3 2 τ τ ¯ $$ E\left(\frac{3}{2},\tau, \overline{\tau}\right) $$ and E 5 2 τ τ ¯ $$ E\left(\frac{5}{2},\tau, \overline{\tau}\right) $$ , respectively. In the flat space limit, these terms match the corresponding terms in the type IIB S-matrix arising from R 4 and D 4 R 4 contact inter-actions, which, for the R 4 case, represents a check of AdS/CFT at finite string coupling. Furthermore, we present striking evidence that these results generalize so that, at order N 1 2 − m $$ {N}^{\frac{1}{2}-m} $$ with integer m ≥ 0, the expansion of the integrated correlator we study is a linear sum of non-holomorphic Eisenstein series with half-integer index, which are manifestly SL(2, ℤ) invariant.http://link.springer.com/article/10.1007/JHEP11(2020)0161/N ExpansionAdS-CFT CorrespondenceConformal Field TheoryScattering Amplitudes |
| spellingShingle | Shai M. Chester Michael B. Green Silviu S. Pufu Yifan Wang Congkao Wen Modular invariance in superstring theory from N $$ \mathcal{N} $$ = 4 super-Yang-Mills Journal of High Energy Physics 1/N Expansion AdS-CFT Correspondence Conformal Field Theory Scattering Amplitudes |
| title | Modular invariance in superstring theory from N $$ \mathcal{N} $$ = 4 super-Yang-Mills |
| title_full | Modular invariance in superstring theory from N $$ \mathcal{N} $$ = 4 super-Yang-Mills |
| title_fullStr | Modular invariance in superstring theory from N $$ \mathcal{N} $$ = 4 super-Yang-Mills |
| title_full_unstemmed | Modular invariance in superstring theory from N $$ \mathcal{N} $$ = 4 super-Yang-Mills |
| title_short | Modular invariance in superstring theory from N $$ \mathcal{N} $$ = 4 super-Yang-Mills |
| title_sort | modular invariance in superstring theory from n mathcal n 4 super yang mills |
| topic | 1/N Expansion AdS-CFT Correspondence Conformal Field Theory Scattering Amplitudes |
| url | http://link.springer.com/article/10.1007/JHEP11(2020)016 |
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