Kac-Moody and Virasoro characters from the perturbative Chern-Simons path integral

127

186

We study aspects of Jackiw-Teitelboim (JT) quantum gravity in two-dimensional nearly de Sitter (dS) spacetime, as well as pure de Sitter quantum gravity in three dimensions. These are each theories of boundary modes, which include a reparameterization field on each connected component of the boundary as well as topological degrees of freedom. In two dimensions, the boundary theory is closely related to the Schwarzian path integral, and in three dimensions to the quantization of coadjoint orbits of the Virasoro group. Using these boundary theories we compute loop corrections to the wavefunction of the universe, and investigate gravitational contributions to scattering.Along the way, we show that JT gravity in dS 2 is an analytic continuation of JT gravity in Euclidean AdS 2 , and that pure gravity in dS 3 is a continuation of pure gravity in Euclidean AdS 3 . We define a genus expansion for de Sitter JT gravity by summing over higher genus generalizations of surfaces used in the Hartle-Hawking construction. Assuming a conjecture regarding the volumes of moduli spaces of such surfaces, we find that the de Sitter genus expansion is the continuation of the recently discovered AdS genus expansion. Then both may be understood as coming from the genus expansion of the same double-scaled matrix model, which would provide a non-perturbative completion of de Sitter JT gravity.

Section: Dsmentioning

confidence: 99%

Section: Jhep06(2020)048mentioning

confidence: 99%

Low-dimensional de Sitter quantum gravity

Cotler

Jensen

Maloney

2020

127

186

“…Although the abelian Chern-Simons theory carries no metric in the bulk, the perturbative contribution to the partition function can be evaluated on Euclidean (thermal) AdS 3 , whose boundary is a torus with modular parameter τ . The 1-loop partition function is then given by that of D left-and right-moving chiral bosons, determined by the vacuum character of the U (1) D × U (1) D current algebra [14], i.e.,…”

Section: Introductionmentioning

confidence: 99%

Gravitational dual of averaged free CFT’s over the Narain lattice

Pérez

Troncoso

2020

It has been recently argued that the averaging of free CFT’s over the Narain lattice can be holographically described through a Chern-Simons theory for U (1)D×U (1)D with a precise prescription to sum over three-dimensional handlebodies. We show that a gravitational dual of these averaged CFT’s would be provided by Einstein gravity on AdS3 with U (1)D−1× U (1)D−1 gauge fields, endowed with a precise set of boundary conditions closely related to the “soft hairy” ones. Gravitational excitations then go along diagonal SL (2, ℝ) generators, so that the asymptotic symmetries are spanned by U (1)D× U (1)D currents. The stress-energy tensor can then be geometrically seen as composite of these currents through a twisted Sugawara construction. Our boundary conditions are such that for the reduced phase space, there is a one-to-one map between the configurations in the gravitational and the purely abelian theories. The partition function in the bulk could then also be performed either from a non-abelian Chern-Simons theory for two copies of SL (2, ℝ) × U (1)D−1 generators, or formally through a path integral along the family of allowed configurations for the metric. The new boundary conditions naturally accommodate BTZ black holes, and the microscopic number of states then appears to be manifestly positive and suitably accounted for from the partition function in the bulk. The inclusion of higher spin currents through an extended twisted Sugawara construction in the context of higher spin gravity is also briefly addressed.

“…One might hope that the presence of the cosmological constant again translates into beneficial infrared regulating properties, similarly to AdS. In this sense these theories also present themselves as interesting testing ground for the calculations of partition functions [72,73] (see also [74][75][76], or [77] for the flat case) and for sharpening our understanding of entanglement entropy, following, e.g., [78,79], in more general set-ups.…”

Section: Three-dimensional Kinematical Theoriesmentioning

confidence: 98%

Limits of three-dimensional gravity and metric kinematical Lie algebras in any dimension

Matulich

Prohazka

Salzer

2019

We extend a recent classification of three-dimensional spatially isotropic homogeneous spacetimes to Chern-Simons theories as three-dimensional gravity theories on these spacetimes. By this we find gravitational theories for all carrollian, galilean, and aristotelian counterparts of the lorentzian theories. In order to define a nondegenerate bilinear form for each of the theories, we introduce (not necessarily central) extensions of the original kinematical algebras. Using the structure of so-called double extensions, this can be done systematically. For homogeneous spaces that arise as a limit of (anti-)de Sitter spacetime, we show that it is possible to take the limit on the level of the action, after an appropriate extension. We extend our systematic construction of nondegenerate bilinear forms also to all higher-dimensional kinematical algebras.