# The 39th International Symposium on Lattice Field Theory (Lattice 2022)

Aug 8 – 13, 2022
Hörsaalzentrum Poppelsdorf
Europe/Berlin timezone

## Chiral Symmetry Breaking in QED induced by an External Magnetic Field

Aug 9, 2022, 2:00 PM
20m
CP1-HSZ/1st-1.001 - HS5 (CP1-HSZ)

### CP1-HSZ/1st-1.001 - HS5

#### CP1-HSZ

50
Oral Presentation Vacuum Structure, Confinement, and Chiral Symmetry

### Speaker

Donald Sinclair (Argonne National Laboratory)

### Description

$3+1$ dimensional QED with massless electrons is chirally symmetric, at least in the perturbative regime. This is true, even though this symmetry is anomalous, because QED lacks instantons. However, in the presence of external magnetic fields, approximate calculations based on Schwinger-Dyson equations indicate that chiral symmetry is spontaneously broken. In a constant external magnetic field $B$, this produces a dynamical electron mass $\propto\sqrt{eB}$ and a chiral condensate $\propto(eB)^{3/2}$. The magnetic field catalyses chiral symmetry breaking with an effective dimensional reduction from $3+1$ dimensions to $1+1$ dimensions. We simulate lattice QED in a constant homogeneous magnetic field using the RHMC algorithm. We increase $\alpha$ from $1/137$ to $1/5$ to make the chiral symmetry breaking measurable. To access the chiral limit, we need to increase the lattice size. By using a large $eB$, the localization of the motion in the plane perpendicular to the magnetic field due to the dominance of low lying Landau levels means that we only need a large lattice size in the directions of $B$ and time. Our preliminary `data' show clear evidence for a non-zero condensate in the zero electron mass limit and hence chiral symmetry breaking.

### Primary author

Donald Sinclair (Argonne National Laboratory)

### Co-author

Dr John Kogut (U. of Maryland, USDOE)