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

Rafał R. Suszek

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arXiv · 1209.2334

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

Rafał R. Suszek

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Abstract

This is the second in a series of papers discussing in the framework of gerbe theory canonical and geometric aspects of the 2d nonlinear sigma model in the presence of conformal defects in the worldsheet. Employing the formal tools worked out in the first paper of the series, 1101.1126 [hep-th], a thorough analysis of rigid symmetries of the sigma model is carried out with emphasis on algebraic structures on generalised tangent bundles over the target space of the theory and over its state space that give rise to a realisation of the symmetry algebra on states. The analysis leads to a proposal for a novel differential-algebraic construct extending the original definition of the (gerbe-twisted) Courant algebroid on the generalised tangent bundles over the target space in a manner codetermined by the structure of the 2-category of abelian bundle gerbes with connection over it. The construct admits a neat interpretation in terms of a relative Cartan calculus associated with the hierarchy of manifolds that compose the target space of the multiphase sigma model. The paper also discusses at length the gauge anomaly for the rigid symmetries, derived and quantified cohomologically in a previous work of Gawȩdzki, Waldorf and the author. The ensuing reinterpretation of the small gauge anomaly in terms of the twisted rel. Courant algebroid modelling the Poisson algebra of Noether charges of the symmetries is elucidated through an equivalence between a category built from data of the gauged sigma model and that of principal bundles over the worldsheet with a structural action groupoid based on the target space. Finally, the large gauge anomaly is identified with the obstruction to the existence of topological defect networks implementing the action of the gauge group of the gauged sigma model and those giving a local trivialisation of a gauge bundle of an arbitrary topology over the worldsheet.

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Rafał R. Suszek. 2012-09-11. Defects, dualities and the geometry of strings via gerbes II. Generalised geometries with a twist, the gauge anomaly and the gauge-symmetry defect. https://arxiv.org/abs/1209.2334

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