Anomaly constraints on gapped phases with discrete chiral symmetry

Abstract

We prove that in ð3 þ 1Þd quantum field theories with Z N symmetry, certain anomalies forbid a symmetry-preserving vacuum state with a gapped spectrum. In particular, this applies to discrete chiral symmetries which are frequently present in gauge theories as we illustrate in examples. Our results also constrain the long-distance behavior of certain condensed matter systems such as Weyl-semimetals and may have applications to crystallographic phases with symmetry protected topological order. These results may be viewed as analogs of the Lieb-Schultz-Mattis theorem for continuum field theories.

Symmetries and strings of adjoint QCD2

“…There has been a lot of progress recently on some aspects of strongly coupled field theory dynamics, and, in particular, gauge theories with adjoint matter in 3 and 4 space-time dimensions. See for instance [2][3][4][5][6][7][8][9][10][11][12][13][14] and references therein.…”

“…A useful additional exercise to carry out before discussing the non-Abelian theory is to add small quartic interactions to (2.7). 13 By "small' what we mean is that it is suppressed by an energy scale much higher than e or m. A possible quartic interaction to contemplate JHEP03(2021)103 is |α|e i arg αΨ +Ψ+ Ψ − Ψ − + c.c.. Another term we can add is βΨ +Ψ− Ψ + Ψ − . The term proportional to β is invariant under both the shift symmetry and the dual shift symmetry, which means that in terms of the variable φ it cannot lead to an interesting potential for φ (it may lead to derivative terms).…”

Deconfinement on axion domain walls

“…We refer to these constraints as "generalized 't Hooft anomalies." Their study is evolving too rapidly to allow us to do justice to all interesting aspects currently investigated; we only note that complementary aspects of theories closely related to the ones we consider here are the subject of [6][7][8][9][10][11][12][13][14][15][16][17][18].…”

Condensates and anomaly cascade in vector-like theories

“…It was discovered in [2,3] that Higher-form symmetries may also become anomalous, which can be used to impose further constraints on strongly-coupled theories. These original papers were followed by a plethora of other works that attempted to use the new anomalies to study various aspects of quantum field theory, see [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] for a non-comprehensive list.…”