Melting Instantons, Domain Walls, and Large N

TL;DR

This paper investigates how topological charge structures in $CP^{N-1}$ models change from small instantons to extended membranes as N increases, revealing a transition relevant to understanding QCD.

Contribution

It demonstrates a sharp transition in topological charge structure at N≈4, from instantons to domain walls, providing insight into large N behavior and instanton melting.

Findings

Topological charge is instanton-dominated for N<4.

For N>4, topological charge forms extended membranes.

The transition is linked to instanton melting and large N QCD phenomena.

Abstract

Monte Carlo studies of $CP^{N-1}$ sigma models have shown that the structure of topological charge in these models undergoes a sharp transition at $N=N_c\approx 4$. For $N<N_c$ topological charge is dominated by small instantons, while for $N>N_c$ it is dominated by extended, thin, 1-dimensionally coherent membranes of topological charge, which can be interpreted as domain walls between discrete quasi-stable vacua. These vacua differ by a unit of background electric flux. The transition can be identified as the delocalization of topological charge, or "instanton melting," a phenomenon first suggested by Witten to resolve the conflict between instantons and large $N$ behavior. Implications for $QCD$ are discussed.