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/

Zendy Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

In the context of Conformal Field Theory (CFT), many results can be obtainedfrom the representation theory of the Virasoro algebra. While the interest inLogarithmic CFTs has been growing recently, the Virasoro representationscorresponding to these quantum field theories remain dauntingly complicated,thus hindering our understanding of various critical phenomena. We extend inthis paper the construction of Read and Saleur (2007), and uncover a deeprelationship between the Virasoro algebra and a finite-dimensional algebracharacterizing the properties of two-dimensional statistical models, theso-called blob algebra (a proper extension of the Temperley--Lieb algebra).This allows us to explore vast classes of Virasoro representations (projective,tilting, generalized staggered modules, etc.), and to conjecture aclassification of all possible indecomposable Virasoro modules (with, inparticular, L_0 Jordan cells of arbitrary rank) that may appear in a consistentphysical Logarithmic CFT where Virasoro is the maximal local chiral algebra. Asby-products, we solve and analyze algebraically quantum-group symmetric XXZspin chains and sl(2|1) supersymmetric spin chains with extra spins at theboundary, together with the "mirror" spin chain introduced by Martin andWoodcock (2004).

A physical approach to the classification of indecomposable Virasoro representations from the blob algebra