When renormalisation remembers: UV/IR mixing as an entanglement bridge
- 1Durham University
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.
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BibTeX
@article{abel2026when,
title = {{When renormalisation remembers: UV/IR mixing as an entanglement bridge}},
author = {Steven Abel},
journal = {Journal of High Energy Physics},
year = {2026},
month = oct,
doi = {10.1007/jhep10(2026)025},
url = {https://link.springer.com/10.1007/JHEP10(2026)025},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - When renormalisation remembers: UV/IR mixing as an entanglement bridge
AU - Steven Abel
PY - 2026
DA - 2026/10/02
JO - Journal of High Energy Physics
DO - 10.1007/jhep10(2026)025
UR - https://link.springer.com/10.1007/JHEP10(2026)025
AB - 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.
SN - 1029-8479
ER -