English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Quantum gravity that describes the world beyond the Planck scale should beformulated in a background-metric independent manner. Such a background-freenature can be represented as a gauge equivalency under conformaltransformations, called the BRST conformal symmetry. In this review, we presentquantum field theories of gravity with such symmetry. Since we can choose anybackground owing to this symmetry as far as it is conformally flat, we hereemploy the cylindrical background. First, we briefly review the famous BRSTLiouville-Virasoro algebra in 2D quantum gravity on $R \times S^1$. We thenpresent recent developments of the BRST conformal algebra and physical statesof 4D quantum gravity on $R \times S^3$ whose conformal-factor dynamics isruled by the Riegert's Wess-Zumino action, which arises in the UV limit of therenormalizable quantum conformal gravity with the "asymptotic backgroundfreedom". We find that the BRST conformal invariance makes all physical statesreal and scalar as well as all negative-metric modes unphysical.  We also briefly discuss the dynamics of how the conformal invariance breaksdown and how our classical spacetime emerges at low energies, in which a novelinterpretation of the "minimal length" we can measure comes out withoutdiscretizing spacetime.

BRST Conformal Symmetry as A Background-Free Nature of Quantum Gravity