Higher Structure Conferences Waldorf

String structures and spin structures on loop spaces

Abstract: Supersymmetric sigma models are 2-dimensional field theories which suffer from a so-called global worldsheet anomaly. Two ways of trivializing this anomaly have been proposed: by Stolz-Teichner using string structures on the target space, and by Killingback using spin structures on its loop space. I will present an enhanced version of Killingbacks spin structures for which the two approaches become equivalent. It incorporates fusion products and thin homotopy equivariance. The main tools are the transgression of 2-gerbes and lifting gerbes.

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