Undergrad Is the Continuum Limit of Spin Foam Dynamics Equivalent to Massless Gravitons?

[ohwilleke]

TL;DR

Spin Foam is a quantum gravity method that quantizes space-time. But a new paper claims that a massless graviton can be inferred from it.

The spin-foam approach to quantum gravity is part of the class of approaches, that also include loop quantum gravity and a variety of other methods, that sets out to quantize space-time rather than the gravitational force itself.

But, according to a new paper, it turns out that "the continuum limit of spin foam dynamics does lead to massless gravitons."

The result is not at all obvious, and the analysis in the linked paper is challenging to follow. But it is also a result that is expected because both spin-foam approaches and graviton based quantum gravity approaches are trying to approximate general relativity. And, general relativity is widely believed to be the classical limit of a quantum theory with a massless spin-2 graviton.

Could it be that at some deep level quantizing space-time, and quantizing gravity in a more or less canonical way with a massless spin-2 graviton, are equivalent, with one implying the other and visa versa?

The March 4, 2022 paper is:

From spin foams to area metric dynamics to gravitons​

Bianca Dittrich, Athanasios Kogios

Although spin foams arose as quantizations of the length metric degrees of freedom, the quantum configuration space is rather based on areas as more fundamental variables. This is also highlighted by the semi-classical limit of four-dimensional spin foam models, which is described by the Area Regge action. Despite its central importance to spin foams the dynamics encoded by the Area Regge action is only poorly understood, in particular in the continuum limit.

We perform here a systematic investigation of the dynamics defined by the Area Regge action on a regular centrally subdivided hypercubical lattice. This choice of lattice avoids many problems of the non-subdivided hypercubical lattice, for which the Area Regge action is singular. The regularity of the lattice allows to extract the continuum limit and its corrections, order by order in the lattice constant.

We show that, contrary to widespread expectations which arose from the so-called flatness problem of spin foams, the continuum limit of the Area Regge action does describe to leading order the same graviton dynamics as general relativity. The next-to-leading order correction to the effective action for the length metric is of second order in the lattice constant, and is given by a quadratic term in the Weyl curvature tensor. This correction can be understood to originate from an underlying dynamics of area metrics.

This suggests that the continuum limit of spin foam dynamics does lead to massless gravitons, and that the leading order quantum corrections can be understood to emerge from a generalization of the configuration space from length to area metrics.

 

[Maarten Havinga]

Good find, thanks for sharing!

 

[kodama]

Bianca Dittrich
Modified general relativity from the continuum limit of effective spin foams
Effective spin foams have been introduced to facilitate the extraction of dynamical information from the spin foam path integral. In this talk I will illustrate that effective spin foams have delivered on this promise: I will review how effective spin foams provided a transparent explanation of how the flatness problem of spin foams is avoided in the discrete. With some assumptions on the spin foam path integral, the effective spin foam approach can be also used to determine the continuum limit of spin foam dynamics. To leading order the dynamics is given by a massless graviton, but includes corrections arising from the emergence of an effective area metric. I will then derive the same dynamics directly from a modified Plebanski action. This does provide strong evidence that spin foams reproduce general relativity in the continuum limit and opens new avenues to study the phenomenological implications of spin foams.

https://indico.cern.ch/event/1100970/page/23817-plenary-talks