1,859 research outputs found
On the homeomorphism groups of manifolds and their universal coverings
Let stand for the path connected identity component of the
group of all compactly supported homeomorphisms of a manifold . It is shown
that is perfect and simple under mild assumptions on .
Next, conjugation-invariant norms on \H_c(M) are considered and the
boundedness of is investigated. Finally, the structure of the
universal covering group of is studied.Comment: 19 page
Charged sectors, spin and statistics in quantum field theory on curved spacetimes
The first part of this paper extends the Doplicher-Haag-Roberts theory of
superselection sectors to quantum field theory on arbitrary globally hyperbolic
spacetimes. The statistics of a superselection sector may be defined as in flat
spacetime and each charge has a conjugate charge when the spacetime possesses
non-compact Cauchy surfaces. In this case, the field net and the gauge group
can be constructed as in Minkowski spacetime.
The second part of this paper derives spin-statistics theorems on spacetimes
with appropriate symmetries. Two situations are considered: First, if the
spacetime has a bifurcate Killing horizon, as is the case in the presence of
black holes, then restricting the observables to the Killing horizon together
with "modular covariance" for the Killing flow yields a conformally covariant
quantum field theory on the circle and a conformal spin-statistics theorem for
charged sectors localizable on the Killing horizon. Secondly, if the spacetime
has a rotation and PT symmetry like the Schwarzschild-Kruskal black holes,
"geometric modular action" of the rotational symmetry leads to a
spin-statistics theorem for charged covariant sectors where the spin is defined
via the SU(2)-covering of the spatial rotation group SO(3).Comment: latex2e, 73 page
Cyclic surfaces and Hitchin components in rank 2
We prove that given a Hitchin representation in a real split rank 2 group
, there exists a unique equivariant minimal surface in the
corresponding symmetric space. As a corollary, we obtain a parametrization of
the Hitchin components by a Hermitian bundle over Teichm\"uller space. The
proof goes through introducing holomorphic curves in a suitable bundle over the
symmetric space of . Some partial extensions of the construction
hold for cyclic bundles in higher rank.Comment: 61 pages v3. Final version, with more typos corrected as well as the
statement of Proposition 6.3.1 (cyclic surfaces as holomorphic curves
Topological Crystalline Bose Insulator in Two Dimensions via Entanglement Spectrum
Strongly correlated analogues of topological insulators have been explored in
systems with purely on-site symmetries, such as time-reversal or charge
conservation. Here, we use recently developed tensor network tools to study a
quantum state of interacting bosons which is featureless in the bulk, but
distinguished from an atomic insulator in that it exhibits entanglement which
is protected by its spatial symmetries. These properties are encoded in a model
many-body wavefunction that describes a fully symmetric insulator of bosons on
the honeycomb lattice at half filling per site. While the resulting integer
unit cell filling allows the state to bypass `no-go' theorems that trigger
fractionalization at fractional filling, it nevertheless has nontrivial
entanglement, protected by symmetry. We demonstrate this by computing the
boundary entanglement spectra, finding a gapless entanglement edge described by
a conformal field theory as well as degeneracies protected by the non-trivial
action of combined charge-conservation and spatial symmetries on the edge.
Here, the tight-binding representation of the space group symmetries plays a
particular role in allowing certain entanglement cuts that are not allowed on
other lattices of the same symmetry, suggesting that the lattice representation
can serve as an additional symmetry ingredient in protecting an interacting
topological phase. Our results extend to a related insulating state of
electrons, with short-ranged entanglement and no band insulator analogue.Comment: 18 pages, 13 figures Added additional reference
- …