Higher geometric aspects of global Double Field Theory

Abstract: Higher differential geometry is a generalization of differential geometry, where ordinary geometric structures are replaced by their L∞-versions (such as L∞groups and L∞algebras). This formalism let the concept of principal bundle be generalized to the one of "bundle gerbe". This geometric object can be equipped with a connection, whose parallel transport is defined on surfaces instead of on paths. This will be exactly the global formalization of the Kalb-Ramond field. We can then say that bundle gerbes are for strings what principal bundles are for gauge particles.

Double Field Theory is often referred to as a generalization of Kaluza-Klein Theory that unifies a metric and a Kalb-Ramond field, instead of a gauge field. Can this statement be made geometrically precise? In this talk I will give a simple introduction to higher differential geometry, then I will explore the idea that DFT can be naturally globalized in this geometric formalism. Finally I will apply this construction to obtain some examples of T-duality.

HEP - theory

Audience: researchers in the topic

Exceptional geometry seminar series

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