Furusawa, Takuya | Search NASA

DOE OSTI2021

Anomaly-induced edge currents in hydrodynamics with parity anomaly

Here in this paper, we discuss relativistic hydrodynamics for a massless Dirac fermion in (2 + 1) dimensions, which has the parity anomaly—a global ’t Hooft anomaly between U(1) and parity symmetries. We investigate how hydrodynamics implements the party anomaly, particularly focusing on the transport phenomena at the boundary. Based on the parity anomaly matching and the second law of local thermodynamics, we find U(1) and entropy currents localized at the boundary, as well as the bulk anomalous current with vanishing divergence. These edge currents are similar to the ( 1 + 1)-dimensional chiral transports, but the coefficients are given by half of theirs. We also generalize our discussion to more general anomalies among multiple U(1) symmetries and single $\mathbb{Z}_2$ symmetry.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Global anomaly matching in the higher-dimensional $\mathbb{CP}^{N–1}$ model

Here, we investigate 't Hooft anomalies in the $\mathbb{CP}^{N–1}$ model in space-time 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 $\mathbb{CP}^{N–1}$ model is also discussed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗