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 Plus annual

Presents the access of premium content as premium feature

Premium Content

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 annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The orbifold construction $A\mapsto A^G$ for a finite group $G$ isfundamental in rational conformal field theory. The construction of $Rep(A^G)$from $Rep(A)$ on the categorical level, often called gauging, is also prominentin the study of topological phases of matter. Given a non-degenerate braidedfusion category $\mathcal{C}$ with a $G$-action, the key step in thisconstruction is to find a braided $G$-crossed extension compatible with theaction. The extension theory of Etingof-Nikshych-Ostrik gives two obstructionsfor this problem, $o_3\in H^3(G)$ and $o_4\in H^4(G)$ for certain coefficients,the latter depending on a categorical lifting of the action and is notoriouslydifficult to compute. We show that in the case where $G\le S_n$ acts bypermutations on $\mathcal{C}^{\boxtimes n}$, both of these obstructions vanish.This verifies a conjecture of M\"uger, and constitutes a nontrivial test of theconjecture that all modular tensor categories come from vertex operatoralgebras or conformal nets.

Vanishing of categorical obstructions for permutation orbifolds