SciPost Phys. 9, 028 (2020) ·
published 1 September 2020

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Scalar unitary representations of the isometry group of $d$dimensional de
Sitter space $SO(1,d)$ are labeled by their conformal weights $\Delta$. A
salient feature of de Sitter space is that scalar fields with sufficiently
large mass compared to the de Sitter scale $1/\ell$ have complex conformal
weights, and physical modes of these fields fall into the unitary continuous
principal series representation of $SO(1,d)$. Our goal is to study these
representations in $d=2$, where the relevant group is $SL(2,\mathbb{R})$. We
show that the generators of the isometry group of dS$_2$ acting on a massive
scalar field reproduce the quantum mechanical model introduced by de Alfaro,
Fubini and Furlan (DFF) in the early/late time limit. Motivated by the ambient
dS$_2$ construction, we review in detail how the DFF model must be altered in
order to accommodate the principal series representation. We point out a
difficulty in writing down a classical Lagrangian for this model, whereas the
canonical Hamiltonian formulation avoids any problem. We speculate on the
meaning of the various de Sitter invariant vacua from the point of view of this
toy model and discuss some potential generalizations.
Tarek Anous, Joanna L. Karczmarek, Eric Mintun, Mark Van Raamsdonk, Benson Way
SciPost Phys. 8, 057 (2020) ·
published 15 April 2020

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The BFSS matrix model provides an example of gaugetheory / gravity duality
where the gauge theory is a model of ordinary quantum mechanics with no spatial
subsystems. If there exists a general connection between areas and entropies in
this model similar to the RyuTakayanagi formula, the entropies must be more
general than the usual subsystem entanglement entropies. In this note, we first
investigate the extremal surfaces in the geometries dual to the BFSS model at
zero and finite temperature. We describe a method to associate regulated areas
to these surfaces and calculate the areas explicitly for a family of surfaces
preserving $SO(8)$ symmetry, both at zero and finite temperature. We then
discuss possible entropic quantities in the matrix model that could be dual to
these regulated areas.
SciPost Phys. 7, 003 (2019) ·
published 4 July 2019

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We use the monodromy method to compute expectation values of an arbitrary
number of light operators in finitely excited ("heavy") eigenstates of
holographic 2D CFT. For eigenstates with scaling dimensions above the BTZ
threshold, these behave thermally up to small corrections, with an effective
temperature determined by the heavy state. Below the threshold we find
oscillatory and not decaying behavior. As an application of these results we
compute the expectation of the outoftime order arrangement of four light
operators in a heavy eigenstate, i.e. a sixpoint function. Above the threshold
we find maximally scrambling behavior with Lyapunov exponent $2\pi T_{\rm
eff}$. Below threshold we find that the eigenstate OTOC shows persistent
harmonic oscillations.
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.
Submissions
Submissions for which this Contributor is identified as an author:
Dr Anous: "Dear Referee, Thank you ag..."
in Report on Parity and the modular bootstrap