Related papers: The "Parity" Anomaly On An Unorientable Manifold
In an analogy to the odd-dimensional case we define the parity anomaly as the part of the one-loop effective action for fermions associated with spectral asymmetry of the Dirac operator. This quantity is computed directly on…
A topological superconductor ring is uniquely characterized by a switch in the ground state fermion number parity upon insertion of one superconducting flux quantum - a direct consequence of the topological `parity anomaly.' Despite the…
't Hooft anomaly matching is powerful for constraining the low energy phases of gauge theories. In 3d one common anomaly is the parity anomaly in a $T$-symmetric theory where one cannot gauge the global symmetry group without breaking the…
Unconventional lattice fermions with high degeneracies beyond Weyl and Dirac fermions have attracted intensive attention in recent years. In this paper, attention is drawn to the pseudospin-1 Maxwell fermions and the $(2+1)$ dimensional…
We use techniques from functorial quantum field theory to provide a geometric description of the parity anomaly in fermionic systems coupled to background gauge and gravitational fields on odd-dimensional spacetimes. We give an explicit…
In this paper we consider gravitational parity anomaly in three and four dimensions. We start with a re-computation of this anomaly on a 3D manifold without boundaries and with a critical comparison of our results to the previous…
One of the interesting features about field theories in odd dimensions is the induction of parity violating terms and well-defined {\em finite} topological actions via quantum loops if a fermion mass term is originally present and…
The physics of a parity anomaly, potentially observable in a narrow-gap semiconductor, is revisited. Fradkin, Dagotto, and Boyanovsky have suggested that a Hall current of anomalous parity can be induced by a Peierls distortion on a domain…
The notion of an odd quasi-connection on a supermanifold, which is loosely an affine connection that carries non-zero Grassmann parity, is examined. Their torsion and curvature are defined, however, in general, they are not tensors. A…
Nodal-line semimetals are topological semimetals characterized by one-dimensional band-touching loops protected by the combined symmetry of inversion $\mathcal{P}$ and time-reversal $\mathcal{T}$ in absence of spin-orbit coupling. These…
It is shown that parity operator plays an interesting role in Dirac equation in (1+2) dimensions and can be used for defining chiral currents. It is shown that the "anomalous" current induced by an external gauge field can be related to the…
The possibility of parity violation in a gravitational theory with torsion is extensively explored in four and higher dimensions. In the former case,we have listed our conclusions on when and whether parity ceases to be conserved, with both…
We develop a theory of anomalies of fermionic topological phases of matter in (2+1)D with a general fermionic symmetry group $G_f$. In general, $G_f$ can be a non-trivial central extension of the bosonic symmetry group $G_b$ by fermion…
We investigate a topological superconducting wire with balanced gain and loss that is effectively described by the non-Hermitian Kitaev/Majorana chain with parity-time symmetry. This system is shown to possess two distinct types of…
Quantum anomalies arise when symmetries of a classical theory cannot be preserved upon quantization, leading to unconventional topological responses. A prominent example is the parity anomaly of a single two-dimensional Dirac fermion, which…
In this letter, we investigate topological phases of full-gapped odd-parity superconductors, which are distinguished by the bulk topological invariants and the topologically protected gapless boundary states. Using the particle-hole…
We review the parity anomaly and a duality web in 2+1 dimensions. An odd dimensional non-interacting Dirac fermion theory is not parity invariant at quantum level. We demonstrate the parity anomaly in a three dimensional non-interacting…
Dirac fermions coupled to gauge fields can exhibit the chiral anomaly even on a finite spatial lattice. A careful description of this phenomenon yields new insights into the nature of spin-charge relations and on-site symmetries (symmetries…
The classification of topological states of matter in terms of unitary symmetries and dimensionality predicts the existence of nontrivial topological states even in zero-dimensional systems, i.e., a system with a discrete energy spectrum.…
The interaction of fermion spin with spacetime can be non-universal, leading to a new interaction beyond the Standard Model, independent of gravitation. Fermions generate spacetime torsion, which can be integrated out in favor of a…