66,377 research outputs found
Bulk-boundary correspondence for three-dimensional symmetry-protected topological phases
We derive a bulk-boundary correspondence for three-dimensional (3D)
symmetry-protected topological (SPT) phases with unitary symmetries. The
correspondence consists of three equations that relate bulk properties of these
phases to properties of their gapped, symmetry-preserving surfaces. Both the
bulk and surface data appearing in our correspondence are defined via a
procedure in which we gauge the symmetries of the system of interest and then
study the braiding statistics of excitations of the resulting gauge theory. The
bulk data is defined in terms of the statistics of bulk excitations, while the
surface data is defined in terms of the statistics of surface excitations. An
appealing property of this data is that it is plausibly complete in the sense
that the bulk data uniquely distinguishes each 3D SPT phase, while the surface
data uniquely distinguishes each gapped, symmetric surface. Our correspondence
applies to any 3D bosonic SPT phase with finite Abelian unitary symmetry group.
It applies to any surface that (1) supports only Abelian anyons and (2) has the
property that the anyons are not permuted by the symmetries.Comment: 31 pages, 14 figures, 1 tabl
Recoverable Information and Emergent Conservation Laws in Fracton Stabilizer Codes
We introduce a new quantity, that we term recoverable information, defined
for stabilizer Hamiltonians. For such models, the recoverable information
provides a measure of the topological information, as well as a physical
interpretation, which is complementary to topological entanglement entropy. We
discuss three different ways to calculate the recoverable information, and
prove their equivalence. To demonstrate its utility, we compute recoverable
information for fracton models using all three methods where appropriate. From
the recoverable information, we deduce the existence of emergent
Gauss-law type constraints, which in turn imply emergent conservation
laws for point-like quasiparticle excitations of an underlying topologically
ordered phase.Comment: Added additional cluster model calculation (SPT example) and a new
section discussing the general benefits of recoverable informatio
Hartle-Hawking Wave-Function for Flux Compactifications
We argue that the topological string partition function, which has been known
to correspond to a wave-function, can be interpreted as an exact
``wave-function of the universe'' in the mini-superspace sector of physical
superstring theory. This realizes the idea of Hartle and Hawking in the context
of string theory, including all loop quantum corrections. The mini-superspace
approximation is justified as an exact description of BPS quantities. Moreover
this proposal leads to a conceptual explanation of the recent observation that
the black hole entropy is the square of the topological string wave-function.
This wave-function can be interpreted in the context of flux compactification
of all spatial dimensions as providing a physical probability distribution on
the moduli space of string compactification. Euclidean time is realized
holographically in this setup.Comment: 37 pages, 2 figure
Complex Networks and Symmetry I: A Review
In this review we establish various connections between complex networks and
symmetry. While special types of symmetries (e.g., automorphisms) are studied
in detail within discrete mathematics for particular classes of deterministic
graphs, the analysis of more general symmetries in real complex networks is far
less developed. We argue that real networks, as any entity characterized by
imperfections or errors, necessarily require a stochastic notion of invariance.
We therefore propose a definition of stochastic symmetry based on graph
ensembles and use it to review the main results of network theory from an
unusual perspective. The results discussed here and in a companion paper show
that stochastic symmetry highlights the most informative topological properties
of real networks, even in noisy situations unaccessible to exact techniques.Comment: Final accepted versio
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