On the Interplay of Monopoles and Chiral Symmetry Breaking in Non-Compact Lattice QED

TL;DR

This study uses lattice QED simulations to explore how monopoles influence chiral symmetry breaking across various fermion flavors, revealing different transition types and supporting the idea that monopoles drive the chiral transition.

Contribution

It provides the first detailed lattice analysis linking monopole behavior with chiral symmetry breaking over a wide range of fermion flavors in non-compact QED.

Findings

Chiral symmetry breaking correlates with monopole percolation.

Second order transitions for Nf between 8 and 16.

First order transitions for Nf between 20 and 32.

Abstract

Non-compact lattice QED is simulated for various numbers of fermion species $N_f$ ranging from 8 through 40 by the exact Hybrid Monte Carlo algorithm. Over this range of $N_f$, chiral symmetry breaking is found to be strongly correlated with the effective monopoles in the theory. For $N_f$ between 8 and 16 the chiral symmetry breaking and monopole percolation transitions are second order and coincident. Assuming powerlaw critical behavior, the correlation length exponent for the chiral transition is identical to that of monopole percolation. This result supports the conjecture that monopole percolation ``drives" the nontrivial chiral transition. For $N_f$ between 20 and 32, the monopoles experience a first order condensation transition coincident with a first order chiral transition. For $N_f$ as large as 40 both transitions are strongly suppressed. The data at large $N_f (N_f \mathrel {\mathpalette \vereq >} 20)$ is interpreted in terms of a strongly interacting monopole gas-liquid transition.