SciPost Phys. 8, 062 (2020) ·
published 17 April 2020

· pdf
Symmetries in Quantum Field Theory may have 't Hooft anomalies. If the
symmetry is unbroken in the vacuum, the anomaly implies a nontrivial lowenergy
limit, such as gapless modes or a topological field theory. If the symmetry is
spontaneously broken, for the continuous case, the anomaly implies lowenergy
theorems about certain couplings of the Goldstone modes. Here we study the case
of spontaneously broken discrete symmetries, such as Z/2 and T. Symmetry
breaking leads to domain walls, and the physics of the domain walls is
constrained by the anomaly. We investigate how the physics of the domain walls
leads to a matching of the original discrete anomaly. We analyze the symmetry
structure on the domain wall, which requires a careful analysis of some
properties of the unbreakable CPT symmetry. We demonstrate the general results
on some examples and we explain in detail the mod 4 periodic structure that
arises in the Z/2 and T case. This gives a physical interpretation for the
Smith isomorphism, which we also extend to more general abelian groups. We show
that via symmetry breaking and the analysis of the physics on the wall, the
computations of certain discrete anomalies are greatly simplified. Using these
results we perform new consistency checks on the infrared phases of 2+1
dimensional QCD.
Zohar Komargodski, Adar Sharon, Ryan Thorngren, Xinan Zhou
SciPost Phys. 6, 003 (2019) ·
published 9 January 2019

· pdf
A natural question about Quantum Field Theory is whether there is a
deformation to a trivial gapped phase. If the underlying theory has an anomaly,
then symmetric deformations can never lead to a trivial phase. We discuss such
discrete anomalies in Abelian Higgs models in 1+1 and 2+1 dimensions. We
emphasize the role of charge conjugation symmetry in these anomalies; for
example, we obtain nontrivial constraints on the degrees of freedom that live
on a domain wall in the VBS phase of the Abelian Higgs model in 2+1 dimensions.
In addition, as a byproduct of our analysis, we show that in 1+1 dimensions the
Abelian Higgs model is dual to the Ising model. We also study variations of the
Abelian Higgs model in 1+1 and 2+1 dimensions where there is no dynamical
particle of unit charge. These models have a center symmetry and additional
discrete anomalies. In the absence of a dynamical unit charge particle, the
Ising transition in the 1+1 dimensional Abelian Higgs model is removed. These
models without a unit charge particle exhibit a remarkably persistent order: we
prove that the system cannot be disordered by either quantum or thermal
fluctuations. Equivalently, when these theories are studied on a circle, no
matter how small or large the circle is, the ground state is nontrivial.
Mr Thorngren: "Dear Colleague, Thank you f..."
in Report on Anomaly Matching in the Symmetry Broken Phase: Domain Walls, CPT, and the Smith Isomorphism