Time-Reversal Symmetry, Anomalies, and Dualities in (2+1)$d$

Abstract

We study continuum quantum field theories in 2+1 dimensions with time-reversal symmetry $\mathcal{T}$. The standard relation ${\mathcal{T}}^2=(-1{)}^F$ is satisfied on all the "perturbative operators" i.e. polynomials in the fundamental fields and their derivatives. However, we find that it is often the case that acting on more complicated operators ${\mathcal{T}}^2=(-1{)}^F\mathcal{M}$ with $\mathcal{M}$ a non-trivial global symmetry. For example, acting on monopole operators, $\mathcal{M}$ could be $\pm 1$ depending on the magnetic charge. We study in detail $U(1)$ gauge theories with fermions of various charges. Such a modification of the time-reversal algebra happens when the number of odd charge fermions is $2\mathrm{mod}4$, e.g. in QED with two fermions. Our work also clarifies the dynamics of QED with fermions of higher charges. In particular, we argue that the long-distance behavior of QED with a single fermion of charge $2$ is a free theory consisting of a Dirac fermion and a decoupled topological quantum field theory. The extension to an arbitrary even charge is straightforward. The generalization of these abelian theories to $SO(N)$ gauge theories with fermions in the vector or in two-index tensor representations leads to new results and new consistency conditions on previously suggested scenarios for the dynamics of these theories. Among these new results is a surprising non-abelian symmetry involving time-reversal.

32 pages, 5 figures. v2: typos corrected, references updated

References in corpus (7)

• Generalized Global Symmetries
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Level/rank Duality and Chern-Simons-Matter Theories
• Chern-Simons-matter dualities with $SO$ and $USp$ gauge groups
• Global Symmetries, Counterterms, and Duality in Chern-Simons Matter Theories with Orthogonal Gauge Groups
• Phases Of Adjoint QCD${}_3$ And Dualities
• Microscopic Theory of Surface Topological Order for Topological Crystalline Superconductors

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• Exceptional Chern-Simons-Matter Dualities
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• Reflections on the Matter of 3d $\mathcal{N}=1$ Vacua and Local $Spin(7)$ Compactifications
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