Stampedes I: Fishnet OPE and Octagon Bootstrap with Nonzero Bridges

Abstract

Some quantities in quantum field theory are dominated by so-called $leadinglogs$ 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 $\mathcal{N}=4$ 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.

33 pages, 18 figures. v1: typos corrected

References in corpus (9)

• Hexagonalization of Correlation Functions
• Structure Constants and Integrable Bootstrap in Planar N=4 SYM Theory
• Determinant formula for the octagon form factor in $\mathcal{N}$=4 SYM
• Ten dimensional symmetry of N=4 SYM correlators
• Lightcone Bootstrap at higher points
• The Wilson Loop -- Large Spin OPE Dictionary
• Decagon at Two Loops
• Hexagonalization of Fishnet integrals I: mirror excitations
• Fishnet four-point integrals: integrable representations and thermodynamic limits

Cited by in corpus (6)

• The Loom for General Fishnet CFTs
• Conformal Four-Point Integrals: Recursive Structure, Toda Equations and Double Copy
• Stampedes II: Null Polygons in Conformal Gauge Theory
• Light-cone limits of large rectangular fishnets
• A Large Twist Limit for Any Operator
• Higher-Point Correlators in N=4 SYM: Ten-Dimensional Null Polygons