# Multi-loop Null Polygons from Fishnet theory to N=4 SYM

### APA

Olivucci, E. (2024). Multi-loop Null Polygons from Fishnet theory to N=4 SYM. Perimeter Institute. https://pirsa.org/24040123

### MLA

Olivucci, Enrico. Multi-loop Null Polygons from Fishnet theory to N=4 SYM. Perimeter Institute, Apr. 30, 2024, https://pirsa.org/24040123

### BibTex

@misc{ pirsa_PIRSA:24040123, doi = {10.48660/24040123}, url = {https://pirsa.org/24040123}, author = {Olivucci, Enrico}, keywords = {Quantum Fields and Strings}, language = {en}, title = {Multi-loop Null Polygons from Fishnet theory to N=4 SYM}, publisher = {Perimeter Institute}, year = {2024}, month = {apr}, note = {PIRSA:24040123 see, \url{https://pirsa.org}} }

Enrico Olivucci Perimeter Institute for Theoretical Physics

## Abstract

"Null Polygons" in N=4 SYM theory describe the multi-point correlators of 1/2-BPS local operators with large R-charge, when they approach the vertices of a light-like polygon. The leading UV divergences of null polygons is conjectured to satisfy a hierarchy of coupled Toda field theory equations [E.O., Vieira ’22]. I will present some progress towards the prediction of Null Polygons beyond leading logarithms via the hexagons technique, appropriately truncated in the light-cone regime. The method, still conjectural, relies on a series of weak-coupling derivations performed in the Fishnet limit of the theory, where the hexagon representation is derived in the basis of eigenfunctions of a conformal Heisenberg magnet in the principal series. I will present a number of worked-out examples for multi-point multi-loop Fishnet Feynman integrals and Null Polygons.

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