Stampedes I: Fishnet OPE and Octagon Bootstrap with Nonzero Bridges

TL;DR

This paper introduces the concept of 'stampedes' as a time-evolution process to understand leading log contributions in quantum field theories, extending bootstrap methods to octagon functions with arbitrary bridges.

Contribution

It presents a novel 'stampede' framework for analyzing leading logs and extends bootstrap techniques to more complex octagon correlators in quantum field theories.

Findings

Stampede dynamics govern leading log quantities in certain QFTs.

Extended bootstrap methods to all octagon functions with arbitrary diagonal bridges.

Applied results to fishnet theory and N=4 SYM correlators.

Abstract

Some quantities in quantum field theory are dominated by so-called $\mathit{leading\,logs}$ and can be re-summed to all loop orders. In this work we introduce a notion of $\mathit{stampede}$ which is a simple time-evolution of a bunch of particles which start their life in a corner - on the very right say - and $\mathit{hop}$ 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 $\mathcal{N}=4$ 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.