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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This is the second in a series of papers discussing in the framework of gerbetheory canonical and geometric aspects of the 2d nonlinear sigma model in thepresence of conformal defects in the worldsheet. Employing the formal toolsworked out in the first paper of the series, 1101.1126 [hep-th], a thoroughanalysis of rigid symmetries of the sigma model is carried out with emphasis onalgebraic structures on generalised tangent bundles over the target space ofthe theory and over its state space that give rise to a realisation of thesymmetry algebra on states. The analysis leads to a proposal for a noveldifferential-algebraic construct extending the original definition of the(gerbe-twisted) Courant algebroid on the generalised tangent bundles over thetarget space in a manner codetermined by the structure of the 2-category ofabelian bundle gerbes with connection over it. The construct admits a neatinterpretation in terms of a relative Cartan calculus associated with thehierarchy of manifolds that compose the target space of the multiphase sigmamodel. The paper also discusses at length the gauge anomaly for the rigidsymmetries, derived and quantified cohomologically in a previous work ofGaw\c{e}dzki, Waldorf and the author. The ensuing reinterpretation of the smallgauge anomaly in terms of the twisted rel. Courant algebroid modelling thePoisson algebra of Noether charges of the symmetries is elucidated through anequivalence between a category built from data of the gauged sigma model andthat of principal bundles over the worldsheet with a structural action groupoidbased on the target space. Finally, the large gauge anomaly is identified withthe obstruction to the existence of topological defect networks implementingthe action of the gauge group of the gauged sigma model and those giving alocal trivialisation of a gauge bundle of an arbitrary topology over theworldsheet.

Defects, dualities and the geometry of strings via gerbes II. Generalised geometries with a twist, the gauge anomaly and the gauge-symmetry defect