Relations between integrated correlators in N = 4 supersymmetric Yang-Mills theory
Integrated correlation functions in N = 4 supersymmetric Yang-Mills theory with gauge group SU(N) can be expressed in terms of the localised S4 partition function, ZN, deformed by a mass m. Two such cases are CN=Imτ2∂τ∂τ¯∂m2logZNm=0 and HN=∂m4logZNm=0, which are modular invariant functions of the co...
| Main Authors: | , , , , |
|---|---|
| Format: | Journal article |
| Language: | English |
| Published: |
Springer
2024
|
| _version_ | 1811140118667329536 |
|---|---|
| author | Alday, LF Chester, SM Dorigoni, D Green, MB Wen, C |
| author_facet | Alday, LF Chester, SM Dorigoni, D Green, MB Wen, C |
| author_sort | Alday, LF |
| collection | OXFORD |
| description | Integrated correlation functions in N = 4 supersymmetric Yang-Mills theory with gauge group SU(N) can be expressed in terms of the localised S4 partition function, ZN, deformed by a mass m. Two such cases are CN=Imτ2∂τ∂τ¯∂m2logZNm=0 and HN=∂m4logZNm=0, which are modular invariant functions of the complex coupling τ. While CN was recently written in terms of a two-dimensional lattice sum for any N and τ, HN has only been evaluated up to order 1/N3 in a large-N expansion in terms of modular invariant functions with no known lattice sum realisation. Here we develop methods for evaluating HN to any desired order in 1/N and finite τ. We use this new data to constrain higher loop corrections to the stress tensor correlator, and give evidence for several intriguing relations between HN and CN to all orders in 1/N. We also give evidence that the coefficients of the 1/N expansion of HN can be written as lattice sums to all orders. Lastly, these large N and finite τ results are used to accurately estimate the integrated correlators at finite N and finite τ. |
| first_indexed | 2024-09-25T04:16:54Z |
| format | Journal article |
| id | oxford-uuid:4f549f1f-e76e-45fa-90c1-b12b0d1360ab |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-09-25T04:16:54Z |
| publishDate | 2024 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:4f549f1f-e76e-45fa-90c1-b12b0d1360ab2024-07-20T14:58:10ZRelations between integrated correlators in N = 4 supersymmetric Yang-Mills theoryJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:4f549f1f-e76e-45fa-90c1-b12b0d1360abEnglishJisc Publications RouterSpringer2024Alday, LFChester, SMDorigoni, DGreen, MBWen, CIntegrated correlation functions in N = 4 supersymmetric Yang-Mills theory with gauge group SU(N) can be expressed in terms of the localised S4 partition function, ZN, deformed by a mass m. Two such cases are CN=Imτ2∂τ∂τ¯∂m2logZNm=0 and HN=∂m4logZNm=0, which are modular invariant functions of the complex coupling τ. While CN was recently written in terms of a two-dimensional lattice sum for any N and τ, HN has only been evaluated up to order 1/N3 in a large-N expansion in terms of modular invariant functions with no known lattice sum realisation. Here we develop methods for evaluating HN to any desired order in 1/N and finite τ. We use this new data to constrain higher loop corrections to the stress tensor correlator, and give evidence for several intriguing relations between HN and CN to all orders in 1/N. We also give evidence that the coefficients of the 1/N expansion of HN can be written as lattice sums to all orders. Lastly, these large N and finite τ results are used to accurately estimate the integrated correlators at finite N and finite τ. |
| spellingShingle | Alday, LF Chester, SM Dorigoni, D Green, MB Wen, C Relations between integrated correlators in N = 4 supersymmetric Yang-Mills theory |
| title | Relations between integrated correlators in N = 4 supersymmetric Yang-Mills theory |
| title_full | Relations between integrated correlators in N = 4 supersymmetric Yang-Mills theory |
| title_fullStr | Relations between integrated correlators in N = 4 supersymmetric Yang-Mills theory |
| title_full_unstemmed | Relations between integrated correlators in N = 4 supersymmetric Yang-Mills theory |
| title_short | Relations between integrated correlators in N = 4 supersymmetric Yang-Mills theory |
| title_sort | relations between integrated correlators in n 4 supersymmetric yang mills theory |
| work_keys_str_mv | AT aldaylf relationsbetweenintegratedcorrelatorsinn4supersymmetricyangmillstheory AT chestersm relationsbetweenintegratedcorrelatorsinn4supersymmetricyangmillstheory AT dorigonid relationsbetweenintegratedcorrelatorsinn4supersymmetricyangmillstheory AT greenmb relationsbetweenintegratedcorrelatorsinn4supersymmetricyangmillstheory AT wenc relationsbetweenintegratedcorrelatorsinn4supersymmetricyangmillstheory |