9,702 research outputs found
Topological string entanglement
We investigate how topological entanglement of Chern-Simons theory is
captured in a string theoretic realization. Our explorations are motivated by a
desire to understand how quantum entanglement of low energy open string degrees
of freedom is encoded in string theory (beyond the oft discussed classical
gravity limit). Concretely, we realize the Chern-Simons theory as the
worldvolume dynamics of topological D-branes in the topological A-model string
theory on a Calabi-Yau target. Via the open/closed topological string duality
one can map this theory onto a pure closed topological A-model string on a
different target space, one which is related to the original Calabi-Yau
geometry by a geometric/conifold transition. We demonstrate how to uplift the
replica construction of Chern-Simons theory directly onto the closed string and
show that it provides a meaningful definition of reduced density matrices in
topological string theory. Furthermore, we argue that the replica construction
commutes with the geometric transition, thereby providing an explicit closed
string dual for computing reduced states, and Renyi and von Neumann entropies
thereof. While most of our analysis is carried out for Chern-Simons on S^3, the
emergent picture is rather general. Specifically, we argue that quantum
entanglement on the open string side is mapped onto quantum entanglement on the
closed string side and briefly comment on the implications of our result for
physical holographic theories where entanglement has been argued to be crucial
ingredient for the emergence of classical geometry.Comment: 48 pages + appendices, many tikz fgures. v2: added clarification
A hierarchy of topological tensor network states
We present a hierarchy of quantum many-body states among which many examples
of topological order can be identified by construction. We define these states
in terms of a general, basis-independent framework of tensor networks based on
the algebraic setting of finite-dimensional Hopf C*-algebras. At the top of the
hierarchy we identify ground states of new topological lattice models extending
Kitaev's quantum double models [26]. For these states we exhibit the mechanism
responsible for their non-zero topological entanglement entropy by constructing
a renormalization group flow. Furthermore it is shown that those states of the
hierarchy associated with Kitaev's original quantum double models are related
to each other by the condensation of topological charges. We conjecture that
charge condensation is the physical mechanism underlying the hierarchy in
general.Comment: 61 page
PEPS as ground states: degeneracy and topology
We introduce a framework for characterizing Matrix Product States (MPS) and
Projected Entangled Pair States (PEPS) in terms of symmetries. This allows us
to understand how PEPS appear as ground states of local Hamiltonians with
finitely degenerate ground states and to characterize the ground state
subspace. Subsequently, we apply our framework to show how the topological
properties of these ground states can be explained solely from the symmetry: We
prove that ground states are locally indistinguishable and can be transformed
into each other by acting on a restricted region, we explain the origin of the
topological entropy, and we discuss how to renormalize these states based on
their symmetries. Finally, we show how the anyonic character of excitations can
be understood as a consequence of the underlying symmetries.Comment: 54 pages, 110 diagrams, 1 figure. v2: minor changes. v3: accepted
version, minor change
BPS Spectra, Barcodes and Walls
BPS spectra give important insights into the non-perturbative regimes of
supersymmetric theories. Often from the study of BPS states one can infer
properties of the geometrical or algebraic structures underlying such theories.
In this paper we approach this problem from the perspective of persistent
homology. Persistent homology is at the base of topological data analysis,
which aims at extracting topological features out of a set of points. We use
these techniques to investigate the topological properties which characterize
the spectra of several supersymmetric models in field and string theory. We
discuss how such features change upon crossing walls of marginal stability in a
few examples. Then we look at the topological properties of the distributions
of BPS invariants in string compactifications on compact threefolds, used to
engineer black hole microstates. Finally we discuss the interplay between
persistent homology and modularity by considering certain number theoretical
functions used to count dyons in string compactifications and by studying
equivariant elliptic genera in the context of the Mathieu moonshine
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