Holographic models of de Sitter QFTs

TL;DR

This work explores strongly coupled quantum field theories on de Sitter backgrounds using holographic duality, focusing on (i) conformal field theories in the static patch at arbitrary $T$ and $H$, and (ii) confining gauge theories engineered by Scherk–Schwarz compactification. It derives regular bulk geometries for CFTs at general $T$ in the static patch and computes their stress tensors, finding no phase transitions as $T/T_{\rm dS}$ varies. For confining theories, it demonstrates a confinement/deconfinement transition driven by cosmological acceleration, with the critical de Sitter temperature satisfying $T_{\rm dS}=T_c/d$ in $d$ dimensions, and analyzes the dual Euclidean saddles (bubble of nothing vs topological AdS black hole) that control this transition. The paper also discusses phase diagrams in the $(T,H)$ plane and outlines approximate interpolations between high-$T$ Minkowski and de Sitter deconfined phases, suggesting avenues for future work on dynamical cosmological transitions and FRW spacetimes. Overall, it provides a holographic framework for dynamical phase structure of strongly coupled QFTs in cosmological backgrounds, with potential implications for early-universe physics.

Abstract

We describe the dynamics of strongly coupled field theories in de Sitter spacetime using the holographic gauge/gravity duality. The main motivation for this is to explore the possibility of dynamical phase transitions during cosmological evolution. Specifically, we study two classes of theories: (i) conformal field theories on de Sitter in the static patch which are maintained in equilibrium at temperatures that may differ from the de Sitter temperature and (ii) confining gauge theories on de Sitter spacetime. In the former case we show the such states make sense from the holographic viewpoint in that they have regular bulk gravity solutions. In the latter situation we add to the evidence for a confinement/deconfinement transition for a large N planar gauge theory as the cosmological acceleration is increased past a critical value. For the field theories we study, the critical acceleration corresponds to a de Sitter temperature which is less than the Minkowski space deconfinement transition temperature by a factor of the spacetime dimension.

Figures (4)

• Figure 1: The geometries relevant for holographic descriptions of confining theories on de Sitter spacetime: (a) the bubble of nothing spacetime in AdS and (b) the Bañados black hole. The outer cylinder in both cases is the AdS boundary. For the bubble of nothing, the part of the spacetime behind the bubble whose trajectory is shown is not part of the spacetime manifold. For the Bañados black hole we have sketched the causal diagram: the singularities are hyperbolae located behind an event horizon ${\cal H}^+ \cup {\cal H}^-$. The curious feature of this solution is that it has a bifurcation point, as opposed to a regular bifurcation surface encountered for more familiar black hole spacetimes. .
• Figure 2: Penrose digram for de Sitter spacetime in $d$ dimensions. The static patch associated with the observer on the north pole of the ${\bf S}^{d-1}$ is shown as the shaded region. Lines of constant $t$ are indicated as the solid (blue) curves. The dashed lines are the cosmological horizons, with ${\cal H}^\pm$ being the future/past cosmological horizons of the static observer.
• Figure 3: The plot of the bulk horizon for the bulk three dimensional geometry (\ref{['ds2HT']}) whose boundary is dS$_{2}$. We plot the location of the horizon in the $\{r,z\}$ coordinates used to express the solution as a solid black line. The static patch of de Sitter is restricted to $|r| \le H^{-1}$ and this is the relevant region of the spacetime even in the bulk. The shaded region lies inside the horizon in the bulk geometry.
• Figure 4: Proposed phase diagram for confining gauge theory on de Sitter spacetime. This thin dashed line represents the de Sitter-invariant state with $T=\frac{1}{2\pi}\, H$. The diagram assumes the absence of phase transitions other than the thick dashed line representing a change in topology of the dual Euclidean solution from ${\bf S}^d \times {\bf R}^2$ to ${\bf R}^{d+1} \times {\bf S}^1$. Also note that the transition temperature does down as we increase the cosmological acceleration.