Stampedes I: fishnet OPE and octagon Bootstrap with nonzero bridges

Some quantities in quantum field theory are dominated by so-called leading logs and can be re-summed to all loop orders. In this work we introduce a notion of stampede which is a simple time-evolution of a bunch of particles which start their life in a corner - on the very right say - and hop their way to the opposite corner - on the left - through the repeated action of a quantum Hamiltonian. Such stampedes govern leading logs quantities in certain quantum field theories. The leading euclidean OPE limit of correlation functions in the fishnet theory and null double-scaling limits of correlators in N = 4 SYM are notable examples. As an application, we use these results to extend the beautiful bootstrap program of Coronado [1] to all octagons functions with arbitrary diagonal bridge length.

Automated summary

Some important quantities in quantum field theory can be re-summed using a concept called stampede, which is a simple time-evolution process of particles. Stampede plays a crucial role in certain quantum field theories, governing leading logarithmic quantities. The leading euclidean OPE limit in fishnet theory and null double-scaling limits in N=4 SYM are notable examples. This work extends a beautiful bootstrap program to all octagon functions with arbitrary diagonal bridge length using these results.