3,334 research outputs found
Spin connection formulations of real Lorentzian General Relativity
We derive the pure spin connection and constraint-free BF formulations of
real four-dimensional Lorentzian vacuum General Relativity. In contrast to the
existing complex formulations, an important advantage is that they do not
require the reality constraints that complicate quantization. We also consider
the corresponding modified gravity theories and point out that, contrary to
their self-dual analogues, they are not viable because they necessarily contain
ghosts. In particular, this constrains the set of potentially viable unified
theories one can build by extending the gauge group to the ones with the action
structure of General Relativity. We find, however, that the resulting theories
do not admit classical solutions. This issue can be solved by introducing extra
dynamical fields which, incidentally, could also provide a way to include a
matter sector.Comment: 20 page
Integrable Matrix Product States from boundary integrability
We consider integrable Matrix Product States (MPS) in integrable spin chains
and show that they correspond to "operator valued" solutions of the so-called
twisted Boundary Yang-Baxter (or reflection) equation. We argue that the
integrability condition is equivalent to a new linear intertwiner relation,
which we call the "square root relation", because it involves half of the steps
of the reflection equation. It is then shown that the square root relation
leads to the full Boundary Yang-Baxter equations. We provide explicit solutions
in a number of cases characterized by special symmetries. These correspond to
the "symmetric pairs" and , where
in each pair the first and second elements are the symmetry groups of the spin
chain and the integrable state, respectively. These solutions can be considered
as explicit representations of the corresponding twisted Yangians, that are new
in a number of cases. Examples include certain concrete MPS relevant for the
computation of one-point functions in defect AdS/CFT.Comment: 33 pages, v2: minor corrections, references added, v3: minor
modifications, v4: minor modification
Visualizing Two Qubits
The notions of entanglement witnesses, separable and entangled states for two
qubits system can be visualized in three dimensions using the SLOCC equivalence
classes. This visualization preserves the duality relations between the various
sets and allows us to give ``proof by inspection'' of a non-elementary result
of the Horodeckies that for two qubits, Peres separability test is iff. We then
show that the CHSH Bell inequalities can be visualized as circles and cylinders
in the same diagram. This allows us to give a geometric proof of yet another
result of the Horodeckies, which optimizes the violation of the CHSH Bell
inequality. Finally, we give numerical evidence that, remarkably, allowing
Alice and Bob to use three rather than two measurements each, does not help
them to distinguish any new entangled SLOCC equivalence class beyond the CHSH
class.Comment: 22 pages, 5 figures. Added several reference
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