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arXiv · 1004.3664

The emergence of geometry: a two-dimensional toy model

Jorge Alfaro·Domènec Espriu·Daniel Puigdomènech
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Abstract

We review the similarities between the effective chiral lagrangrian, relevant for low-energy strong interactions, and the Einstein-Hilbert action. We use these analogies to suggest a specific mechanism whereby gravitons would emerge as Goldstone bosons of a global SO(D) X GL(D) symmetry broken down to SO(D) by fermion condensation. We propose a two-dimensional toy model where a dynamical zwei-bein is generated from a topological theory without any pre-existing metric structure, the space being endowed only with an affine connection. A metric appears only after the symmetry breaking; thus the notion of distance is an induced effective one. In spite of several non-standard features this simple toy model appears to be renormalizable and at long distances is described by an effective lagrangian that corresponds to that of two-dimensional gravity (Liouville theory). The induced cosmological constant is related to the dynamical mass M acquired by the fermion fields in the breaking, which also acts as an infrared regulator. The low-energy expansion is valid for momenta k >M, i.e. for supra-horizon scales. We briefly discuss a possible implementation of a similar mechanism in four dimensions.

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Jorge Alfaro, Domènec Espriu, Daniel Puigdomènech. 2010-04-21. The emergence of geometry: a two-dimensional toy model. https://doi.org/10.1103/physrevd.82.045018

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