45 research outputs found
FRW cosmologies and hyperscaling-violating geometries: higher curvature corrections, ultrametricity, Q-space/QFT duality, and a little string theory
We analyze flat FRW cosmologies and hyperscaling-violating geometries by
emphasizing the analytic continuation between them and their scale covariance.
We exhibit two main calculations where this point of view is useful. First,
based on the scale covariance, we show that the structure of higher curvature
corrections to Einstein's equation is very simple. Second, in the context of
accelerated FRW cosmologies, also known as Q-space, we begin by calculating the
Bunch-Davies wavefunctional for a massless scalar field and considering its
interpretation as a generating functional of correlation functions of a
holographic dual. We use this to conjecture a Q-space/QFT duality, a natural
extension of dS/CFT, and argue that the Euclidean dual theory violates
hyperscaling. This proposal, when extended to epochs in our own cosmological
history like matter or radiation domination, suggests a holographically dual
description via RG phases which violate hyperscaling. We further use the
wavefunctional to compute Anninos-Denef overlaps and show that the ultrametric
structure discovered for de Sitter becomes sharper in accelerated FRW
cosmologies as the acceleration slows. The substitution permeates and illuminates the discussion of wavefunctionals
and overlaps in FRW cosmologies, allowing one to predict the sharpened
structure. We try to find an alternate manifestation of this ultrametric
structure by studying the connection of the background to
little string theory.Comment: 31 pages plus an appendix; v2 references added; v3 discussion of
generalized extreme value distributions added and typos correcte
Detachable circles and temperature-inversion dualities for CFT
We use a Weyl transformation between and to relate a conformal field theory at arbitrary
temperature on to itself at the inverse temperature on
. We use this equivalence to deduce a confining
phase transition at finite temperature for large- gauge theories on
hyperbolic space. In the context of gauge/gravity duality, this equivalence
provides new examples of smooth bulk solutions which asymptote to conically
singular geometries at the AdS boundary. We also discuss implications for the
Eguchi-Kawai mechanism and a high-temperature/low-temperature duality on
.Comment: 21 page
Warped Entanglement Entropy
We study the applicability of the covariant holographic entanglement entropy
proposal to asymptotically warped AdS spacetimes with an SL(2,R) x U(1)
isometry. We begin by applying the proposal to locally AdS backgrounds
which are written as a real-line fibration over AdS. We then perturb away
from this geometry by considering a warping parameter to get an
asymptotically warped AdS spacetime and compute the dual entanglement
entropy perturbatively in . We find that for large separation in the
fiber coordinate, the entanglement entropy can be computed to all orders in
and takes the universal form appropriate for two-dimensional CFTs. The
warping-dependent central charge thus identified exactly agrees with previous
calculations in the literature. Performing the same perturbative calculations
for the warped BTZ black hole again gives universal two-dimensional CFT
answers, with the left-moving and right-moving temperatures appearing
appropriately in the result.Comment: 25 pages plus appendices; v2 references added, discussions clarified
and equations sharpene
Parity and the modular bootstrap
We consider unitary, modular invariant, two-dimensional CFTs which are
invariant under the parity transformation . Combining with modular
inversion leads to a continuous family of fixed points of the
transformation. A particular subset of this locus of fixed points exists along
the line of positive left- and right-moving temperatures satisfying . We use this fixed locus to prove a conjecture of Hartman,
Keller, and Stoica that the free energy of a large- CFT with a suitably
sparse low-lying spectrum matches that of AdS 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 when . At large we show that the operator
dimension of the first excited primary lies in a region in the
-plane that is significantly smaller than
. Our results for the free energy and constraints on the
operator spectrum extend to theories without parity symmetry through the
construction of an auxiliary parity-invariant partition function.Comment: 21 pages, 3 figures, v2 reference and equation added, v3 minor edits
and figure 2 improve