8,404 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
Quasi-B-mode generated by high-frequency gravitational waves and corresponding perturbative photon fluxes
Interaction of very low-frequency primordial(relic) gravitational waves(GWs)
to cosmic microwave background(CMB) can generate B-mode polarization. Here, for
the first time we point out that the electromagnetic(EM) response to
high-frequency GWs(HFGWs) would produce quasi-B-mode distribution of the
perturbative photon fluxes, and study the duality and high complementarity
between such two B-modes. Based on this quasi-B-mode in HFGWs, it is shown that
the distinguishing and observing of HFGWs from the braneworld would be quite
possible due to their large amplitude, higher frequency and very different
physical behaviors between the perturbative photon fluxes and background
photons, and the measurement of relic HFGWs may also be possible though face to
enormous challenge.Comment: 22 pages, 6 figures, research articl
A local maximum principle for robust optimal control problems of quadratic BSDEs
The paper concerns the necessary maximum principle for robust optimal control
problems of quadratic BSDEs. The coefficient of the systems depends on the
parameter , and the generator of BSDEs is of quadratic growth in .
Since the model is uncertain, the variational inequality is proved by weak
convergence technique. In addition, due to the generator being quadratic with
respect to , the forward adjoint equations are SDEs with unbounded
coefficient involving mean oscillation martingales. Using reverse H\"older
inequality and John-Nirenberg inequality, we show that its solutions are
continuous with respect to the parameter . The necessary and sufficient
conditions for robust optimal control are proved by linearization method.Comment: 35 page
The Oblique Corrections from Heavy Scalars in Irreducible Representations
The contributions to , , and from heavy scalars in any irreducible
representation of the electroweak gauge group are
obtained. We find that in the case of a heavy scalar doublet there is a slight
difference between the parameter we have obtained and that in previous
works.Comment: 6 pages, 2 axodraw figures; minor changes, references update
Electromagnetic counterparts of high-frequency gravitational waves having additional polarization states: distinguishing and probing tensor-mode, vector-mode and scalar-mode gravitons
GWs from extra dimensions, very early universe, and some high-energy
astrophysical process, might have at most six polarizations: plus- and
cross-type (tensor-mode gravitons), x-, y-type (vector-mode), and b-, l-type
(scalar-mode). Peak or partial peak regions of some of such GWs are just
distributed in GHz or higher frequency band, which would be optimal band for
electromagnetic(EM) response. In this paper we investigate EM response to such
high-frequency GWs(HFGWs) having additional polarizations. For the first time
we address:(1)concrete forms of analytic solutions for perturbed EM fields
caused by HFGWs having all six possible polarizations in background stable EM
fields; (2)perturbed EM signals of HFGWs with additional polarizations in
three-dimensional-synchro-resonance-system(3DSR system) and in
galactic-extragalactic background EM fields. These perturbative EM fields are
actually EM counterparts of HFGWs, and such results provide a novel way to
simultaneously distinguish and display all possible six polarizations. It is
also shown: (i)In EM response, pure cross-, x-type and pure y-type
polarizations can independently generate perturbative photon fluxes(PPFs,
signals), while plus-, b- and l-type polarizations produce PPFs in different
combination states. (ii) All such six polarizations have separability and
detectability. (iii)In EM response to HFGWs from extra-dimensions,
distinguishing and displaying different polarizations would be quite possible
due to their very high frequencies, large energy densities and special
properties of spectrum. (iv)Detection band(10^8 to 10^12 Hz or higher) of PPFs
by 3DSR and observation range(7*10^7 to 3*10^9 Hz) of PPFs by FAST
(Five-hundred-meter-Aperture-Spherical Telescope, China), have a certain
overlapping property, so their coincidence experiments will have high
complementarity.Comment: 27 pages, 16 figure
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