2,606 research outputs found
Fractionalization and Anomalies in Symmetry-Enriched U(1) Gauge Theories
We classify symmetry fractionalization and anomalies in a (3+1)d U(1) gauge
theory enriched by a global symmetry group . We find that, in general, a
symmetry-enrichment pattern is specified by 4 pieces of data: , a map
from to the duality symmetry group of this gauge theory
which physically encodes how the symmetry permutes the fractional excitations,
, the symmetry actions
on the electric charge, ,
indication of certain domain wall decoration with bosonic integer quantum Hall
(BIQH) states, and a torsor over , the
symmetry actions on the magnetic monopole. However, certain choices of are not physically realizable, i.e. they are anomalous. We find
that there are two levels of anomalies. The first level of anomalies obstruct
the fractional excitations being deconfined, thus are referred to as the
deconfinement anomaly. States with these anomalies can be realized on the
boundary of a (4+1)d long-range entangled state. If a state does not suffer
from a deconfinement anomaly, there can still be the second level of anomaly,
the more familiar 't Hooft anomaly, which forbids certain types of symmetry
fractionalization patterns to be implemented in an on-site fashion. States with
these anomalies can be realized on the boundary of a (4+1)d short-range
entangled state. We apply these results to some interesting physical examples.Comment: are welcome; v2 references adde
Topological gauge theory, symmetry fractionalization, and classification of symmetry-enriched topological phases in three dimensions
Symmetry plays a crucial role in enriching topological phases of matter.
Phases with intrinsic topological order that are symmetric are called
symmetry-enriched topological phases (SET). In this paper, we focus on SETs in
three spatial dimensions, where the intrinsic topological orders are described
by Abelian gauge theory and the symmetry groups are also Abelian. As a series
work of our previous research [Phys. Rev. B 94, 245120 (2016);
(arXiv:1609.00985)], we study these topological phases described by twisted
gauge theories with global symmetry and consider all possible topologically
inequivalent "charge matrices". Within each equivalence class, there is a
unique pattern of symmetry fractionalization on both point-like and string-like
topological excitations. In this way, we classify Abelian topological order
enriched by Abelian symmetry within our field-theoretic approach. To
illustrate, we concretely calculate many representative examples of SETs and
discuss future directions
N′-Diphenylmethylene-2-hydroxybenzohydrazide
The title compound, C20H16N2O2, was synthesized by the reaction of 2-hydroxybenzohydrazide with diphenylmethanone. The dihedral angle between the phenyl rings is 76.28 (11)°. The amino H atom is involved in an intramolecular N—H⋯O hydrogen bond. In the crystal structure, the hydroxy groups and carbonyl O atoms form intermolecular O—H⋯O hydrogen bonds, which link the molecules into chains running along the b axis
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