PIRSA:20050050

Projective elliptic genera and applications

APA

Han, F. (2020). Projective elliptic genera and applications. Perimeter Institute. https://pirsa.org/20050050

MLA

Han, Fei. Projective elliptic genera and applications. Perimeter Institute, May. 25, 2020, https://pirsa.org/20050050

BibTex

          @misc{ pirsa_20050050,
            doi = {10.48660/20050050},
            url = {https://pirsa.org/20050050},
            author = {Han, Fei},
            keywords = {Mathematical physics},
            language = {en},
            title = {Projective elliptic genera and applications},
            publisher = {Perimeter Institute},
            year = {2020},
            month = {may},
            note = {PIRSA:20050050 see, \url{https://pirsa.org}}
          }
          

Fei Han National University of Singapore

Abstract

Projective vector bundles (or gerbe modules) are generalizations of vector bundles in the presence of a gerbe on manifolds. Given a projective vector bundle, we will first show how to use it to twist the Witten genus to get modular invariants, which we call projective elliptic genera. Then we will give two applications: (1) given any pseudodifferential operator, we will construct modular invariants generalizing the Witten genus, which corresponds to the Dirac operator; (2) we will enhance the Hori map in T-duality to the graded Hori map and show that it sends Jacobi forms to Jacobi forms. This represents our joint works with Mathai.