Asymptotics of the Infrared

TL;DR

This paper introduces a novel scheme for analyzing quantum critical phenomena by evaluating partition function zeroes through a factored quantum loop operator basis, linking renormalization group flows to operator structures.

Contribution

It presents a new method for computing partition function zeroes using quantum loop operators, connecting RG beta-functions to noncommuting operator bases in a finite Hilbert space.

Findings

Partition function zeroes can be derived from factored quantum loop operators.

The approach maps RG beta-functions onto local operator bases.

The method explains CP-violation and complex action problems via zero distribution analyticity.

Abstract

We follow recent formulations of dimensionally reduced loop operators for quantum field theories and exact representations of probabilistic lattice dynamics to identify a new scheme for the evaluation of partition function zeroes, allowing for the explicit analysis of quantum critical phenomena. This new approach gives partition function zeroes from a factored quantum loop operator basis and, as we show, constitutes an effective mapping of the renormalization group $\beta$-function onto the noncommuting local operator basis of a countably finite Hilbert space. The Vafa-Witten theorem for CP-violation and related complex action problems of Euclidean Field theories are discussed, following recent treatments, and are shown to be natural consequences of the analyticity of the limiting distribution of these zeroes, and properties of vacuum regimes governed by a dominant quantum fluctuation in the vicinity of a renormalization group equation fixed point in the infrared.