21 research outputs found
A Type Approximation of the Crossed Product
I show that an analog of the crossed product construction that takes type
algebras to type algebras exists also in the type case. This
is particularly natural when the local algebra is a non-trivial direct sum of
type factors. Concretely, I rewrite the usual type trace in a different
way and renormalise it. This new renormalised trace stays well-defined even
when each factor is taken to be type . I am able to recover both type
as well as type algebras by imposing different
constraints on the central operator in the code. An example of this structure
appears in holographic quantum error-correcting codes; the central operator is
then the area operator.Comment: 15 pages, 3 figure
On The Entanglement Entropy For Gauge Theories
We propose a definition for the entanglement entropy of a gauge theory on a
spatial lattice. Our definition applies to any subset of links in the lattice,
and is valid for both Abelian and Non-Abelian gauge theories. For
and theories, without matter, our definition agrees with
a particular case of the definition given by Casini, Huerta and Rosabal. We
also argue that in general, both for Abelian and Non-Abelian theories, our
definition agrees with the entanglement entropy calculated using a definition
of the replica trick. Our definition, however, does not agree with some
standard ways to measure entanglement, like the number of Bell pairs which can
be produced by entanglement distillation.Comment: 29 pages, 4 figures; section on Extended Lattice Construction revised
and some changes in referencing; some of the discussion of the replica trick
changed; section on SU(2) revised for clarit
Scalar Asymptotic Charges and Dual Large Gauge Transformations
In recent years soft factorization theorems in scattering amplitudes have
been reinterpreted as conservation laws of asymptotic charges. In gauge,
gravity, and higher spin theories the asymptotic charges can be understood as
canonical generators of large gauge symmetries. Such a symmetry interpretation
has been so far missing for scalar soft theorems. We remedy this situation by
treating the massless scalar field in terms of a dual two-form gauge field. We
show that the asymptotic charges associated to the scalar soft theorem can be
understood as generators of large gauge transformations of the dual two-form
field.
The dual picture introduces two new puzzles: the charges have very unexpected
Poisson brackets with the fields, and the monopole term does not always have a
dual gauge transformation interpretation. We find analogs of these two
properties in the Kramers-Wannier duality on a finite lattice, indicating that
the free scalar theory has new edge modes at infinity that canonically commute
with all the bulk degrees of freedom.Comment: 16 pages, 2 figure
Islands with Gravitating Baths: Towards ER = EPR
We study the Page curve and the island rule for black holes evaporating into
gravitating baths, with an eye towards establishing a connection with the
ER=EPR proposal. We consider several models of two entangled 2d black holes in
Jackiw-Teitelboim (JT) gravity with negative cosmological constant. The first,
"doubled PSSY," model is one in which the black holes have end-of-the-world
(ETW) branes with a flavour degree of freedom. We study highly entangled states
of this flavour degree of freedom and find an entanglement-induced
Hawking-Page-like transition from a geometry with two disconnected black holes
to one with a pair of black holes connected by a wormhole, thus realising the
ER = EPR proposal. The second model is a dynamical one in which the ETW branes
do not have internal degrees of freedom but the JT gravity is coupled to a 2d
CFT, and we entangle the black holes by coupling the two CFTs at the
boundary and evolving for a long time. We study the entanglement entropy
between the two black holes and find that the story is substantially similar to
that with a non-gravitating thermal bath. In the third model, we couple the two
ends of a two-sided eternal black hole and evolve for a long time. Finally, we
discuss the possibility of a Hawking-Page-like transition induced by real-time
evolution that realises the ER = EPR proposal in this dynamical setting.Comment: 47+14 pages, 16 figures. Comments welcom
On the Dynamics of Near-Extremal Black Holes
We analyse the dynamics of near-extremal Reissner-Nordstr\"om black holes in
asymptotically four-dimensional Anti-de Sitter space (AdS). We work in the
spherically symmetric approximation and study the thermodynamics and the
response to a probe scalar field. We find that the behaviour of the system, at
low energies and to leading order in our approximations, is well described by
the Jackiw-Teitelboim (JT) model of gravity. In fact, this behaviour can be
understood from symmetry considerations and arises due to the breaking of time
reparametrisation invariance. The JT model has been analysed in considerable
detail recently and related to the behaviour of the SYK model. Our results
indicate that features in these models which arise from symmetry considerations
alone are more general and present quite universally in near-extremal black
holes.Comment: 44 (=26+18) pages, 1 figure, 6 appendices; v2: references added; v3:
minor changes made; v4: additional references added, version accepted in JHE