SciPost Phys. 9, 045 (2020) ·
published 5 October 2020

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We study density matrices in quantum gravity, focusing on topology change. We
argue that the inclusion of braket wormholes in the gravity path integral is
not a free choice, but is dictated by the specification of a global state in
the multiuniverse Hilbert space. Specifically, the HartleHawking (HH) state
does not contain braket wormholes. It has recently been pointed out that
braket wormholes are needed to avoid potential bagsofgold and strong
subadditivity paradoxes, suggesting a problem with the HH state. Nevertheless,
in regimes with a single large connected universe, approximate braket
wormholes can emerge by tracing over the unobserved universes. More drastic
possibilities are that the HH state is nonperturbatively gauge equivalent to a
state with braket wormholes, or that the thirdquantized Hilbert space is
onedimensional. Along the way we draw some helpful lessons from the wellknown
relation between worldline gravity and KleinGordon theory. In particular, the
commutativity of boundarycreating operators, which is necessary for
constructing the alpha states and having a dual ensemble interpretation, is
subtle. For instance, in the worldline gravity example, the KleinGordon field
operators do not commute at timelike separation.
SciPost Phys. 9, 001 (2020) ·
published 1 July 2020

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It has been suggested in recent work that the Page curve of Hawking radiation
can be recovered using computations in semiclassical gravity provided one
allows for "islands" in the gravity region of quantum systems coupled to
gravity. The explicit computations so far have been restricted to black holes
in twodimensional JackiwTeitelboim gravity. In this note, we numerically
construct a fivedimensional asymptotically AdS geometry whose boundary
realizes a fourdimensional HartleHawking state on an eternal AdS black hole
in equilibrium with a bath. We also numerically find two types of extremal
surfaces: ones that correspond to having or not having an island. The version
of the information paradox involving the eternal black hole exists in this
setup, and it is avoided by the presence of islands. Thus, recent computations
exhibiting islands in twodimensional gravity generalize to higher dimensions
as well.
SciPost Phys. 7, 065 (2019) ·
published 26 November 2019

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The existence of higherspin quantum conserved currents in two dimensions
guarantees quantum integrability. We revisit the question of whether
classicallyconserved local higherspin currents in twodimensional sigma
models survive quantization. We define an integrability index $\mathcal{I}(J)$
for each spin $J$, with the property that $\mathcal{I}(J)$ is a lower bound on
the number of quantum conserved currents of spin $J$. In particular, a positive
value for the index establishes the existence of quantum conserved currents.
For a general coset model, with or without extra discrete symmetries, we derive
an explicit formula for a generating function that encodes the indices for all
spins. We apply our techniques to the $\mathbb{CP}^{N1}$ model, the $O(N)$
model, and the flag sigma model $\frac{U(N)}{U(1)^{N}}$. For the $O(N)$ model,
we establish the existence of a spin6 quantum conserved current, in addition
to the wellknown spin4 current. The indices for the $\mathbb{CP}^{N1}$ model
for $N>2$ are all nonpositive, consistent with the fact that these models are
not integrable. The indices for the flag sigma model $\frac{U(N)}{U(1)^{N}}$
for $N>2$ are all negative. Thus, it is unlikely that the flag sigma models are
integrable.
SciPost Phys. 5, 022 (2018) ·
published 11 September 2018

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We consider unitary, modular invariant, twodimensional CFTs which are
invariant under the parity transformation $P$. Combining $P$ with modular
inversion $S$ leads to a continuous family of fixed points of the $SP$
transformation. A particular subset of this locus of fixed points exists along
the line of positive left and rightmoving temperatures satisfying $\beta_L
\beta_R = 4\pi^2$. We use this fixed locus to prove a conjecture of Hartman,
Keller, and Stoica that the free energy of a large$c$ CFT$_2$ with a suitably
sparse lowlying spectrum matches that of AdS$_3$ gravity at all temperatures
and all angular potentials. We also use the fixed locus to generalize the
modular bootstrap equations, obtaining novel constraints on the operator
spectrum and providing a new proof of the statement that the twist gap is
smaller than $(c1)/12$ when $c>1$. At large $c$ we show that the operator
dimension of the first excited primary lies in a region in the
$(h,\overline{h})$plane that is significantly smaller than
$h+\overline{h}<c/6$. Our results for the free energy and constraints on the
operator spectrum extend to theories without parity symmetry through the
construction of an auxiliary parityinvariant partition function.
Dr Mahajan: "Thank you for the report. We h..."
in Report on Entanglement islands in higher dimensions