Maximal U(1) Y -violating n-point correlators in N $$ \mathcal{N} $$ = 4 super-Yang-Mills theory
Abstract This paper concerns a special class of n-point correlation functions of operators in the stress tensor supermultiplet of N $$ \mathcal{N} $$ = 4 supersymmetric SU(N) Yang-Mills theory. These are “maximal U(1) Y -violating” correlators that violate the bonus U(1) Y charge by a maximum of 2(n...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2021-02-01
|
| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP02(2021)042 |
| _version_ | 1819058782246797312 |
|---|---|
| author | Michael B. Green Congkao Wen |
| author_facet | Michael B. Green Congkao Wen |
| author_sort | Michael B. Green |
| collection | DOAJ |
| description | Abstract This paper concerns a special class of n-point correlation functions of operators in the stress tensor supermultiplet of N $$ \mathcal{N} $$ = 4 supersymmetric SU(N) Yang-Mills theory. These are “maximal U(1) Y -violating” correlators that violate the bonus U(1) Y charge by a maximum of 2(n − 4) units. We will demonstrate that such correlators satisfy SL(2, ℤ)-covariant recursion relations that relate n-point correlators to (n − 1)-point correlators in a manner analogous to the soft dilaton relations that relate the corresponding amplitudes in flat-space type IIB superstring theory. These recursion relations are used to determine terms in the large-N expansion of n-point maximal U(1) Y -violating correlators in the chiral sector, including correlators with four superconformal stress tensor primaries and (n − 4) chiral Lagrangian operators, starting from known properties of the n = 4 case. We concentrate on the first three orders in 1/N beyond the supergravity limit. The Mellin representations of the correlators are polynomials in Mellin variables, which correspond to higher derivative contact terms in the low-energy expansion of type IIB superstring theory in AdS 5 × S 5 at the same orders as R 4 , d 4 R 4 and d 6 R 4. The coupling constant dependence of these terms is found to be described by non-holomorphic modular forms with holomorphic and anti-holomorphic weights (n − 4, 4 − n) that are SL(2, ℤ)-covariant derivatives of Eisenstein series and certain generalisations. This determines a number of non-leading contributions to U(1) Y -violating n-particle interactions (n > 4) in the low-energy expansion of type IIB superstring amplitudes in AdS 5 × S 5. |
| first_indexed | 2024-12-21T14:00:40Z |
| format | Article |
| id | doaj.art-e6cac2afa4fd46a0950c47e014eb544c |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-21T14:00:40Z |
| publishDate | 2021-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-e6cac2afa4fd46a0950c47e014eb544c2022-12-21T19:01:22ZengSpringerOpenJournal of High Energy Physics1029-84792021-02-012021215810.1007/JHEP02(2021)042Maximal U(1) Y -violating n-point correlators in N $$ \mathcal{N} $$ = 4 super-Yang-Mills theoryMichael B. Green0Congkao Wen1Department of Applied Mathematics and Theoretical PhysicsSchool of Physics and Astronomy, Queen Mary University of LondonAbstract This paper concerns a special class of n-point correlation functions of operators in the stress tensor supermultiplet of N $$ \mathcal{N} $$ = 4 supersymmetric SU(N) Yang-Mills theory. These are “maximal U(1) Y -violating” correlators that violate the bonus U(1) Y charge by a maximum of 2(n − 4) units. We will demonstrate that such correlators satisfy SL(2, ℤ)-covariant recursion relations that relate n-point correlators to (n − 1)-point correlators in a manner analogous to the soft dilaton relations that relate the corresponding amplitudes in flat-space type IIB superstring theory. These recursion relations are used to determine terms in the large-N expansion of n-point maximal U(1) Y -violating correlators in the chiral sector, including correlators with four superconformal stress tensor primaries and (n − 4) chiral Lagrangian operators, starting from known properties of the n = 4 case. We concentrate on the first three orders in 1/N beyond the supergravity limit. The Mellin representations of the correlators are polynomials in Mellin variables, which correspond to higher derivative contact terms in the low-energy expansion of type IIB superstring theory in AdS 5 × S 5 at the same orders as R 4 , d 4 R 4 and d 6 R 4. The coupling constant dependence of these terms is found to be described by non-holomorphic modular forms with holomorphic and anti-holomorphic weights (n − 4, 4 − n) that are SL(2, ℤ)-covariant derivatives of Eisenstein series and certain generalisations. This determines a number of non-leading contributions to U(1) Y -violating n-particle interactions (n > 4) in the low-energy expansion of type IIB superstring amplitudes in AdS 5 × S 5.https://doi.org/10.1007/JHEP02(2021)0421/N ExpansionAdS-CFT CorrespondenceConformal Field TheoryScattering Amplitudes |
| spellingShingle | Michael B. Green Congkao Wen Maximal U(1) Y -violating n-point correlators in N $$ \mathcal{N} $$ = 4 super-Yang-Mills theory Journal of High Energy Physics 1/N Expansion AdS-CFT Correspondence Conformal Field Theory Scattering Amplitudes |
| title | Maximal U(1) Y -violating n-point correlators in N $$ \mathcal{N} $$ = 4 super-Yang-Mills theory |
| title_full | Maximal U(1) Y -violating n-point correlators in N $$ \mathcal{N} $$ = 4 super-Yang-Mills theory |
| title_fullStr | Maximal U(1) Y -violating n-point correlators in N $$ \mathcal{N} $$ = 4 super-Yang-Mills theory |
| title_full_unstemmed | Maximal U(1) Y -violating n-point correlators in N $$ \mathcal{N} $$ = 4 super-Yang-Mills theory |
| title_short | Maximal U(1) Y -violating n-point correlators in N $$ \mathcal{N} $$ = 4 super-Yang-Mills theory |
| title_sort | maximal u 1 y violating n point correlators in n mathcal n 4 super yang mills theory |
| topic | 1/N Expansion AdS-CFT Correspondence Conformal Field Theory Scattering Amplitudes |
| url | https://doi.org/10.1007/JHEP02(2021)042 |
| work_keys_str_mv | AT michaelbgreen maximalu1yviolatingnpointcorrelatorsinnmathcaln4superyangmillstheory AT congkaowen maximalu1yviolatingnpointcorrelatorsinnmathcaln4superyangmillstheory |