English

Time-Reversal Breaking in QCD$_4$, Walls, and Dualities in 2+1 Dimensions

High Energy Physics - Theory 2018-03-14 v2 Strongly Correlated Electrons

Abstract

We study SU(N)SU(N) Quantum Chromodynamics (QCD) in 3+1 dimensions with NfN_f degenerate fundamental quarks with mass mm and a θ\theta-parameter. For generic mm and θ\theta the theory has a single gapped vacuum. However, as θ\theta is varied through θ=π\theta=\pi for large mm there is a first order transition. For Nf=1N_f=1 the first order transition line ends at a point with a massless η\eta' particle (for all NN) and for Nf>1N_f>1 the first order transition ends at m=0m=0, where, depending on the value of NfN_f, the IR theory has free Nambu-Goldstone bosons, an interacting conformal field theory, or a free gauge theory. Even when the 4d4d bulk is smooth, domain walls and interfaces can have interesting phase transitions separating different 3d3d phases. These turn out to be the phases of the recently studied 3d3d Chern-Simons matter theories, thus relating the dynamics of QCD4_4 and QCD3_3, and, in particular, making contact with the recently discussed dualities in 2+1 dimensions. For example, when the massless 4d4d theory has an SU(Nf)SU(N_f) sigma model, the domain wall theory at low (nonzero) mass supports a 3d3d massless CPNf1CP^{N_f-1} nonlinear σ\sigma-model with a Wess-Zumino term, in agreement with the conjectured dynamics in 2+1 dimensions.

Keywords

Cite

@article{arxiv.1708.06806,
  title  = {Time-Reversal Breaking in QCD$_4$, Walls, and Dualities in 2+1 Dimensions},
  author = {Davide Gaiotto and Zohar Komargodski and Nathan Seiberg},
  journal= {arXiv preprint arXiv:1708.06806},
  year   = {2018}
}

Comments

32 pages. v2: references added, improved discussion of anomalies in Chern-Simons theories