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 $d --> d_{eff}=d-\theta$ 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 $\theta --> -\infty$ 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 CFTd_d

We use a Weyl transformation between $S^1 \times S^{d-1}$ and $S^1 \times \mathcal{H}^{d-1}/\mathbb{Z}$ to relate a conformal field theory at arbitrary temperature on $S^{d-1}$ to itself at the inverse temperature on $\mathcal{H}^{d-1}/\mathbb{Z}$. We use this equivalence to deduce a confining phase transition at finite temperature for large-$N$ 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 $S^{d-1}$.Comment: 21 page

Warped Entanglement Entropy

We study the applicability of the covariant holographic entanglement entropy proposal to asymptotically warped AdS$_3$ spacetimes with an SL(2,R) x U(1) isometry. We begin by applying the proposal to locally AdS$_3$ backgrounds which are written as a real-line fibration over AdS$_2$. We then perturb away from this geometry by considering a warping parameter $a=1+\delta$ to get an asymptotically warped AdS$_3$ spacetime and compute the dual entanglement entropy perturbatively in $\delta$. We find that for large separation in the fiber coordinate, the entanglement entropy can be computed to all orders in $\delta$ 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 $P$. 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 right-moving 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 low-lying 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 $(c-1)/12$ 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 parity-invariant partition function.Comment: 21 pages, 3 figures, v2 reference and equation added, v3 minor edits and figure 2 improve