We study the phase diagram of two-flavor massless two-color QCD (QC 2 D) under the presence of quark chemical potentials and imaginary isospin chemical potentials. At the special point of the imaginary isospin chemical potential, called the isospin Roberge-Weiss (RW) point, two-flavor QC 2 D enjoys the Z 2 center symmetry that acts on both quark flavors and the Polyakov loop. We find a Z 2 't Hooft anomaly of this system, which involves the Z 2 center symmetry, the baryon-number symmetry, and the isospin chiral symmetry. Anomaly matching, therefore, constrains the possible phase diagram at any temperatures and quark chemical potentials at the isospin RW point, and we compare it with previous results obtained by chiral effective field theory and lattice simulations. We also point out an interesting similarity of two-flavor massless QC 2 D with (2+1)-dimensional quantum antiferromagnetic systems.

We investigate 't Hooft anomalies in the CP N −1 model in spacetime dimensions higher than two and identify two types of anomalies: One is a mixed anomaly between the PSU(N ) flavor-rotation and magnetic symmetries, and the other is between the reflection and magnetic symmetries. The latter indicates that even in the absence of the flavor symmetry, the model cannot have a unique gapped ground state as long as the reflection and magnetic symmetries are respected. We also clarified the condition for the 't Hooft anomalies to survive under monopole deformations, which explicitly break the magnetic symmetry down to its discrete subgroup. Besides, we explicitly show how the identified 't Hooft anomalies match in the low-energy effective description of symmetry broken phases-the Néel, U(1) spin liquid, and the valence bond solid phases. An application to the finite-temperature phase diagram of the four-dimensional CP N −1 model is also discussed.

Dualities provide deep insight into physics by relating two seemingly distinct theories. Here we propose and elaborate on a novel duality between bosonic and fermionic theories in four spacetime dimensions. Starting with a Euclidean lattice action consisting of bosonic and fermionic degrees of freedom and integrating out one of them alternatively, we derive a UV duality between a Wilson fermion with self-interactions and an XY model coupled to a compact U(1) gauge field. We find a continuous phase transition between topological and trivial insulators on the fermion side corresponding to Higgs and confinement phases on the boson side. The continuum limit of each lattice theory then leads to an IR duality between a free Dirac fermion and a scalar QED with the vacuum angle π. The resulting bosonic theory proves to incorporate a scalar boson and dyons as low-energy degrees of freedom and it is their three-body composite that realizes the Dirac fermion of the fermionic theory.

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