Non-perturbative de Sitter Jackiw-Teitelboim gravity

TL;DR

The paper develops a non-perturbative formulation of de Sitter JT gravity by summing over (-,-) constant-curvature spacetimes with a carefully chosen path-integral measure and iε prescription. It shows the genus expansion is governed by a purely imaginary string coupling, yielding alternating signs that render the series Borel–Le Roy resumable, and demonstrates that dS JT is the analytic continuation of AdS JT with a negative effective number of degrees of freedom, akin to a matrix model dual. Additionally, the authors establish a topological-recursion structure for dS amplitudes, relate them to a PSL(2;ℝ) BF formulation, and discuss doubly non-perturbative corrections via de Sitter analogues of the Airy model, highlighting subtle aspects of de Sitter holography and potential higher-dimensional extensions.

Abstract

With non-perturbative de Sitter gravity and holography in mind, we deduce the genus expansion of de Sitter Jackiw-Teitelboim (dS JT) gravity. We find that this simple model of quantum cosmology has an effective string coupling which is pure imaginary. This imaginary coupling gives rise to alternating signs in the genus expansion of the dS JT S-matrix, which as a result appears to be Borel-Le Roy resummable. Furthermore dS JT gravity is formally an analytic continuation of AdS JT gravity, and behaves like a matrix integral with a negative number of degrees of freedom.

Figures (5)

• Figure 1: A depiction of the sphere, disk (Hartle-Hawking), and cylinder (global dS$_2$) amplitudes, as well as the inner product on single-boundary asymptotic states.
• Figure 2: Two different complex time contours for the dS JT Hartle-Hawing geometry. The red contour corresponds to half of global dS$_2$, glued to half of a Euclidean hemisphere, while the metric on the blue contour is that of the hyperbolic disk in $(-,-)$ signature. Both contours connect the endpoints $t=i\pi/2$ and $t\to\infty$.
• Figure 3: A schematic of a higher-genus geometry included in the dS JT path integral. It is described by a hyperbolic metric in $(-,-)$ signature, which then has $R = 2$, and we take the boundary 'inverse temperatures' $\beta$ to be pure imaginary with infinitesimally negative real part, as required by the the boundary conditions of dS JT gravity.
• Figure 4: A complex time contour for the geometry in Fig. \ref{['fig:minusminus1']} so that the geometry is asymptotically Lorentzian but has a $(-,-)$ signature region at intermediate times.
• Figure 5: A conceptual depiction of the amplitude $S_{g,p,q}$. On the left-hand side, we represent the amplitude as a sum over $(-,-)$ metrics on a genus $g$ surface with $n=p+q$ boundaries. On the right-hand side we interpret that amplitude as an initial state of $q$ large circles in the far past evolved to the bulk using $\widehat{V}^{\dagger}$. Then time evolution acts with a bulk operator $\widehat{\mathcal{O}}$ that maps the $q$ incoming universes to $p$ outgoing universes, which are then evolved forward using $\widehat{V}$.