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

There are many deep and useful theorems relating Schramm-Loewner evolution(SLE$_\kappa$) and Liouville quantum gravity ($\gamma$-LQG) in the case whenthe parameters satisfy $\kappa \in \{\gamma^2, 16/\gamma^2\}$. Roughlyspeaking, these theorems say that the SLE$_\kappa$ curve cuts the $\gamma$-LQGsurface into two or more independent $\gamma$-LQG surfaces. We extend thesetheorems to the case when $\kappa \not\in \{\gamma^2, 16/\gamma^2\}$. Roughlyspeaking we show that if we have an appropriate variant of SLE$_\kappa$ and anindependent $\gamma$-LQG disk, then the SLE curve cuts the LQG disk into two ormore $\gamma$-LQG surfaces which are conditionally independent given the valuesalong the SLE curve of a certain collection of auxiliary imaginary geometryfields, viewed modulo conformal coordinate change. These fields are sampledindependently from the SLE and the LQG and have the property that that the sumof the central charges associated with the SLE$_\kappa$ curve, the $\gamma$-LQGsurface, and the auxiliary fields is 26. This condition on the central chargeis natural from the perspective of bosonic string theory. We also proveanalogous statements when the SLE curve is replaced by, e.g., an LQG metricball or a Brownian motion path. Statements of this type were conjectured bySheffield and are continuum analogs of certain Markov properties of randomplanar maps decorated by two or more statistical physics models. We include asubstantial list of open problems.

Cutting $\gamma$-Liouville quantum gravity by Schramm-Loewner evolution for $\kappa \not\in \{\gamma^2, 16/\gamma^2\}$