Two-Form Gravity and the Generation of Space-Time

TL;DR

This paper calculates the one-loop effective potential in two-form gravity, revealing a unique minimum that could explain the emergence of space-time from quantum effects at the Planck scale.

Contribution

It provides the first calculation of the one-loop effective potential for the conformal factor in two-form gravity, highlighting a potential mechanism for space-time generation.

Findings

Identifies a non-trivial minimum in the effective potential.

Discovers a quartically divergent term not removable by renormalization.

Suggests a link between the minimum and the Planck scale.

Abstract

In the framework of the two-form gravity, which is classically equivalent to the Einstein gravity, the one-loop effective potential for the conformal factor of metric is calculated in the finite volume and in the finite temperature by choosing a temporal gauge condition. There appears a quartically divergent term which cannot be removed by the renormalization of the cosmological term and we find there is only one non-trivial minimum in the effective potential. If the cut-off scale has a physical meaning, \eg the Planck scale coming from string theory, this minimum might explain why the space-time is generated, \ie why the classical metric has a non-trivial value.