4D beyond-cohomology topological phase protected by $C_2$ symmetry and its boundary theories

Abstract

We study bosonic symmetry protected topological (SPT) phases with $C_2$ rotational symmetry in four spatial dimensions which is not captured by the group cohomology classification. By using the topological crystal approach, we show that the topological crystalline state of this SPT phase is given by placing an $E_8$ state on the two dimensional rotational invariant plane, which provides a simple physical picture of this phase. Based on this understanding, we show that a variant of QED4 with charge-1 and charge-3 Dirac fermions is a field theoretical description of the three dimensional boundary. We also discuss the connection to symmetric gapped boundary with topological order and its anomaly signature.

6 pages, 1 figure

References in corpus (12)

• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Crystalline Insulators
• Topology of crystalline insulators and superconductors
• New classes of topological crystalline insulators with unpinned surface Dirac cones
• Z2-topology in nonsymmorphic crystalline insulators: Mobius twist in surface states
• Construction of bosonic symmetry-protected-trivial states and their topological invariants via $G\times SO(\infty )$ non-linear $\sigma$-models
• Anyon condensation and a generic tensor-network construction for symmetry protected topological phases
• Framed Wilson Operators, Fermionic Strings, and Gravitational Anomaly in 4d
• An Exactly Solvable Model for a $4+1D$ Beyond-Cohomology Symmetry Protected Topological Phase
• Construction and classification of point group symmetry protected topological phases in 2D interacting fermionic systems
• A series of (2+1)d Stable Self-Dual Interacting Conformal Field Theories
• Bound states of three fermions forming symmetry-protected topological phases

Cited by in corpus (6)

• Real-space construction of crystalline topological superconductors and insulators in 2D interacting fermionic systems
• Intrinsically Interacting Higher-Order Topological Superconductors
• Effective field theories of topological crystalline insulators and topological crystals
• Strongly correlated crystalline higher-order topological phases in two-dimensional systems: A coupled-wire study
• Topological invariants beyond symmetry indicators: Boundary diagnostics for twofold rotationally symmetric superconductors
• Gapped boundary of (4+1)d beyond-cohomology bosonic SPT phase