Nina Javerzat, Sebastian Grijalva, Alberto Rosso, Raoul Santachiara
SciPost Phys. 9, 050 (2020) ·
published 12 October 2020

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We consider discrete random fractal surfaces with negative Hurst exponent
$H<0$. A random colouring of the lattice is provided by activating the sites at
which the surface height is greater than a given level $h$. The set of
activated sites is usually denoted as the excursion set. The connected
components of this set, the level clusters, define a oneparameter ($H$) family
of percolation models with longrange correlation in the site occupation. The
level clusters percolate at a finite value $h=h_c$ and for $H\leq\frac{3}{4}$
the phase transition is expected to remain in the same universality class of
the pure (i.e. uncorrelated) percolation. For $\frac{3}{4}<H< 0$ instead,
there is a line of critical points with continously varying exponents. The
universality class of these points, in particular concerning the conformal
invariance of the level clusters, is poorly understood. By combining the
Conformal Field Theory and the numerical approach, we provide new insights on
these phases. We focus on the connectivity function, defined as the probability
that two sites belong to the same level cluster. In our simulations, the
surfaces are defined on a lattice torus of size $M\times N$. We show that the
topological effects on the connectivity function make manifest the conformal
invariance for all the critical line $H<0$. In particular, exploiting the
anisotropy of the rectangular torus ($M\neq N$), we directly test the presence
of the two components of the traceless stressenergy tensor. Moreover, we probe
the spectrum and the structure constants of the underlying Conformal Field
Theory. Finally, we observed that the corrections to the scaling clearly point
out a breaking of integrability moving from the pure percolation point to the
longrange correlated one.
SciPost Phys. 9, 046 (2020) ·
published 5 October 2020

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We extend our exploration of nonstandard continuum quantum field theories in
2+1 dimensions to 3+1 dimensions. These theories exhibit exotic global
symmetries, a peculiar spectrum of charged states, unusual gauge symmetries,
and surprising dualities. Many of the systems we study have a known lattice
construction. In particular, one of them is a known gapless fracton model. The
novelty here is in their continuum field theory description. In this paper, we
focus on models with a global $U(1)$ symmetry and in a followup paper we will
study models with a global $\mathbb{Z}_N$ symmetry.
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.