From “Glueballs” to Massive Strings: Solving N=4 Super-Yang-Mills

by Dr Julius Julius (ENS)

Wednesday 11 Jun 2025, 16:00 → 18:00 Europe/Berlin

 I will describe recent progress in the study of conformal field theory (CFT)-data of planar N=4 Super-Yang-Mills theory at strong coupling. Firstly, I will recap the results obtained using the integrability-based quantum spectral curve which make manifest the spectrum of the spectrum of short massive strings in the flat-space limit of Anti de Sitter (AdS) space. Analysis of the obtained spectrum will then reveal interesting structures: a curious classification of Kaluza-Klein (KK) towers using the eigenvalue of the quadratic Casimir. 

 

Then I will show how the spectral information can be combined with constraints obtained from recent computations of AdS curvature corrections to the flat space four-graviton (Virasoro-Shapiro) amplitude, to extract predictions for leading order three-point functions of a graviton, its KK-mode and a massive string at strong coupling. Here we will notice an intriguing feature: some massive string states have vanishing three-point functions with gravitons and KK modes at the leading order, unlike other states with the same mass-level and spin. We observe this phenomenon for a number of examples, and for entire KK towers of massive string states. This suggests an emergent selection rule at strong coupling. 

 

Then, I will turn towards a similar analysis, but this time for massive string states organised on Regge trajectories. Again using the inputs described above, this time complemented with assumptions based on analyticity of CFT-data in spin, I will describe how the leading order three-point functions can be unmixed on the sub-leading Regge trajectories at strong coupling. Next, including some ad hoc assumptions, we will again see the possibility of an entire Regge trajectory of massive string states decoupling from the Virasoro-Shapiro amplitude. This adds further credence to the possibility of an emergent selection rule at strong coupling. I will then conclude with a discussion on how to interpret/explain/probe further this potentially interesting emergent phenomenon.