Global anomaly matching in the higher-dimensional CPN−1 model

Abstract

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.

Global 3-group symmetry and ’t Hooft anomalies in axion electrodynamics

“…Another application of higher-form symmetries is that Abelian topologically ordered phases [57][58][59][60] can be regarded as broken phases of higher-form symmetries [42,47,49], in which the charged object is a worldline of an anyon. One can further classify phases of gauge theories based on those symmetries [61][62][63][64][65][66][67][68][69][70][71][72][73]. Thus, it becomes possible to understand phenomena of extended objects in terms of higher-form symmetries.…”

“…In contrast, the AB effect in the gapped phase can be understood as a 2-form symmetry, where the charged object is a worldsheet of a vortex line. The higher-form symmetries have been applied to various systems in quantum field theories [59,61,[64][65][66][67][68][69][70][71][72][73][74][75][76][77].…”

Sigma-model analysis of $SU(3)$ antiferromagnetic spins on the triangular lattice

“…Thanks to theoretical developments of symmetry-protected topological (SPT) phases, we now obtain much deep understandings of anomaly matching condition [46][47][48][49][50] (see, for example, Refs. [51][52][53][54][55][56][57][58][59][60][61][62][63][64][65] for some of recent applications).…”

Anomaly-induced edge currents in hydrodynamics with parity anomaly

“…The former allows us to discuss subtle global anomalies involving discrete [4] and higher-form symmetries [5]. These new anomalies impose nontrivial constraints on low-energy behaviors of various systems in high-energy [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] and condensed matter physics [4,[24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41]. On the other hand, a theory with an 't Hooft anomaly emerges on a boundary of the corresponding SPT phase, which is described by a topological field theory in higher spacetime dimensions.…”