Relations between integrated correlators in N = 4 supersymmetric Yang-Mills theory

Alday, Luis F.; Chester, Shai M.; Dorigoni, Daniele; Green, Michael B.; Wen, Congkao

Abstract

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.

Citation

Alday, L. F., Chester, S. M., Dorigoni, D., Green, M. B., & Wen, C. (2024). Relations between integrated correlators in N = 4 supersymmetric Yang-Mills theory. Journal of High Energy Physics, 2024(5), Article 44. https://doi.org/10.1007/jhep05%282024%29044

• Journal Article Type: Article
• Acceptance Date: Mar 25, 2024
• Online Publication Date: May 6, 2024
• Publication Date: May 6, 2024
• Deposit Date: May 13, 2024
• Publicly Available Date: May 13, 2024
• Journal: Journal of High Energy Physics
• Print ISSN: 1126-6708
• Electronic ISSN: 1029-8479
• Publisher: Scuola Internazionale Superiore di Studi Avanzati (SISSA)
• Peer Reviewed: Peer Reviewed
• Volume: 2024
• Issue: 5
• Article Number: 44
• DOI: https://doi.org/10.1007/jhep05%282024%29044
• Keywords: 1/N Expansion, AdS-CFT Correspondence, Duality in Gauge Field Theories, Supersymmetric Gauge Theory
• Public URL: https://durham-repository.worktribe.com/output/2437339