3,268 research outputs found
Algebraic higher symmetry and categorical symmetry -- a holographic and entanglement view of symmetry
We introduce the notion of algebraic higher symmetry, which generalizes
higher symmetry and is beyond higher group. We show that an algebraic higher
symmetry in a bosonic system in -dimensional space is characterized and
classified by a local fusion -category. We find another way to describe
algebraic higher symmetry by restricting to symmetric sub Hilbert space where
symmetry transformations all become trivial. In this case, algebraic higher
symmetry can be fully characterized by a non-invertible gravitational anomaly
(i.e. an topological order in one higher dimension). Thus we also refer to
non-invertible gravitational anomaly as categorical symmetry to stress its
connection to symmetry. This provides a holographic and entanglement view of
symmetries. For a system with a categorical symmetry, its gapped state must
spontaneously break part (not all) of the symmetry, and the state with the full
symmetry must be gapless. Using such a holographic point of view, we obtain (1)
the gauging of the algebraic higher symmetry; (2) the classification of
anomalies for an algebraic higher symmetry; (3) the equivalence between classes
of systems, with different (potentially anomalous) algebraic higher symmetries
or different sets of low energy excitations, as long as they have the same
categorical symmetry; (4) the classification of gapped liquid phases for
bosonic/fermionic systems with a categorical symmetry, as gapped boundaries of
a topological order in one higher dimension (that corresponds to the
categorical symmetry). This classification includes symmetry protected trivial
(SPT) orders and symmetry enriched topological (SET) orders with an algebraic
higher symmetry.Comment: 61 pages, 31 figure
An improved method to test the Distance--Duality relation
Many researchers have performed cosmological-model-independent tests for the
distance duality (DD) relation. Theoretical work has been conducted based on
the results of these tests. However, we find that almost all of these tests
were perhaps not cosmological-model-independent after all, because the distance
moduli taken from a given type Ia supernovae (SNe Ia) compilation are dependent
on a given cosmological model and Hubble constant. In this Letter, we overcome
these defects and by creating a new cosmological-model-independent test for the
DD relation. We use the original data from the Union2 SNe Ia compilation and
the angular diameter distances from two galaxy cluster samples compiled by De
Filippis et al. and Bonamente et al. to test the DD relation. Our results
suggest that the DD relation is compatible with observations, and the spherical
model is slightly better than the elliptical model at describing the intrinsic
shape of galaxy clusters if the DD relation is valid. However, these results
are different from those of previous work.Comment: 5 pages, 2 figures, published on ApJ
Tannaka-Krein duality for finite 2-groups
Let be a finite 2-group. We show that the 2-category
of finite semisimple 2-representations is a
symmetric fusion 2-category. We also relate the auto-equivalence 2-group of the
symmetric monoidal forgetful 2-functor to the auto-equivalence 2-group of the regular algebra and show
that they are equivalent to . This result categorifies the usual
Tannaka-Krein duality for finite groups.Comment: 15 pages. Comments are welcom
Direct reconstruction of dynamical dark energy from observational Hubble parameter data
Reconstructing the evolution history of the dark energy equation of state
parameter directly from observational data is highly valuable in
cosmology, since it contains substantial clues in understanding the nature of
the accelerated expansion of the Universe. Many works have focused on
reconstructing using Type Ia supernova data, however, only a few studies
pay attention to Hubble parameter data. In the present work, we explore the
merit of Hubble parameter data and make an attempt to reconstruct from
them through the principle component analysis approach. We find that current
Hubble parameter data perform well in reconstructing ; though, when
compared to supernova data, the data are scant and their quality is worse. Both
CDM and evolving models can be constrained within at
redshifts
and even at redshifts 0.1 z 1 by
using simulated data of observational quality.Comment: 25 pages, 11 figure
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