Potential Topography and Mass Generation

TL;DR

This paper introduces a systematic approach to understanding exponential decay of correlation functions in asymptotically free theories, analyzing configuration space metrics and potential energy, with applications to QCD and nonlinear sigma models.

Contribution

It presents a novel, systematic framework for analyzing correlation decay without relying on conjectured mechanisms, applying it to QCD and nonlinear sigma models.

Findings

No gap exists in the 1+1-dimensional O(2) model at weak coupling.

A new strong/weak-coupling duality is identified in the O(3) model.

Proposals are outlined for understanding the spectrum in these theories.

Abstract

We describe an approach to understanding exponential decay of correlation functions in asymptotically free theories. This approach is systematic; it does not start from any conjectured mechanism or picture. We begin by studying the metric on the space of configurations and the behavior of the potential-energy function on this space. We describe how these ideas fit in the framework of QCD, as discussed earlier by one of us (P.O.). We then consider the 1+1-dimensional O(2) and O(3) nonlinear sigma models and show that no gap exists in the former at weak coupling. In the O(3) model a new kind of strong/weak-coupling duality is realized. We briefly outline our proposals for understanding the spectrum.