Year: 2026
Type: article
Abstract: A bstract Renormalisation is traditionally understood to be a Wilsonian memoryless process in which ultraviolet (UV) degrees of freedom gradually decouple, leaving an autonomous infrared (IR) description. However this need not be the case: in UV/IR mixed theories correlations between widely separated scales can persist. In this work I recast UV/IR mixing as a Hilbert-space phenomenon, realised as correlations across renormalisation scales. This formulation is implemented using the Born-Reciprocal Tensor Network (BRTN), a new configuration of tensor network that is globally symmetric under phase-space reciprocity. On this network I prepare the vacuum and reproduce the expected radiative corrections. The resulting renormalisation geometry exhibits memory, with a bridge linking reciprocal representations of IR physics, whose cross-bridge entanglement provides a precise criterion for the viability of an effective description. I analyse when this criterion is met, and show that there is a large-volume limit, with the fundamental scale held fixed, in which the obstruction to a local description dilutes: Wilsonian behaviour is restored and renormalisation forgets. The BRTN therefore provides a concrete and calculable platform for UV/IR mixing.
Source: Journal of High Energy Physics
Author: Steven Abel
Institution: Durham University
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7164988645