Holographic description of boundary gravitons in (3+1) dimensions

Abstract

Gravity is uniquely situated in between classical topological field theories and standard local field theories. This can be seen in the the quasi-local nature of gravitational observables, but is nowhere more apparent than in gravity's holographic formulation. Holography holds promise for simplifying computations in quantum gravity. While holographic descriptions of three-dimensional spacetimes and of spacetimes with a negative cosmological constant are well-developed, a complete boundary description of zero curvature, four-dimensional spacetime is not currently available. Building on previous work in three-dimensions, we provide a new route to four-dimensional holography and its boundary gravitons. Using Regge calculus linearized around a flat Euclidean background with the topology of a solid hyper-torus, we obtain the effective action for a dual boundary theory which describes the dynamics of the boundary gravitons. Remarkably, in the continuum limit and at large radii this boundary theory is local and closely analogous to the corresponding result in threedimensions. The boundary effective action has a degenerate kinetic term that leads to singularities in the one-loop partition function that are independent of the discretization. These results establish a rich boundary dynamics for four-dimensional flat holography. * Electronic address: sasanteATperimeterinstitute.ca † Electronic address: bdittrichATperimeterinstitute.ca ‡ Electronic address: haggardATbard.edu

Holographic Formulation of 3D Metric Gravity with Finite Boundaries

“…The method to construct holographic duals directly from gravity, which we employed here, will allow us to study the 4D case. In this regard a first step has been taken in [32]. Here a geodesic effective action has been computed for a 4D generalization of twisted thermal flat space.…”

“…Here a geodesic effective action has been computed for a 4D generalization of twisted thermal flat space. For this [32] restricted to boundary conditions which impose flat perturbations, that is excluded propagating bulk gravitons. The resulting boundary action is then however a straightforward generalization of the 3D result, that is given by the same action with a Liouville like coupling to the boundary Ricci scalar and a degenerate kinetic term.…”

“…Thus the question arises whether these constructions can be also applied to 4D gravity. A first step to answer this question can be found in [32], which uses again (linearized) Regge calculus to consider a background spacetime, which is a 4D version of twisted thermal flat space. Restricting to boundary data which induce a 4D flat solution, [32] finds the same type of boundary theory as in 3D.…”

“…A first step to answer this question can be found in [32], which uses again (linearized) Regge calculus to consider a background spacetime, which is a 4D version of twisted thermal flat space. Restricting to boundary data which induce a 4D flat solution, [32] finds the same type of boundary theory as in 3D. However, due to the fact that 4D Regge calculus does not feature a local discretization independent measure [33], it is hard to extend this result to the (one-loop) quantum theory.…”

“…One can consider a model for quantum flat space[34], for which a discretization independent model does exist. In this case one can compute the one-loop partition function[32], which captures the effect of the boundary degrees of freedom 3. We consider boundaries with homogeneous intrinsic curvature ∂A 2 R = 0 and with non-vanishing extrinsic curvature.…”