Department of

January 2020 February 2020 March 2020 Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa 1 2 3 4 1 1 2 3 4 5 6 7 5 6 7 8 9 10 11 2 3 4 5 6 7 8 8 9 10 11 12 13 14 12 13 14 15 16 17 18 9 10 11 12 13 14 15 15 16 17 18 19 20 21 19 20 21 22 23 24 25 16 17 18 19 20 21 22 22 23 24 25 26 27 28 26 27 28 29 30 31 23 24 25 26 27 28 29 29 30 31

Monday, February 24, 2020

**Abstract:** This talk will concern advances in understanding explicitly the Bagger-Witten line bundle appearing in four-dimensional N=1 supergravity, which is closely related to the Hodge line bundle on a moduli space of Calabi-Yaus. This has recently been a subject of interest, but explicit examples have proven elusive in the past. In this talk we will outline some recent advances, including (1) a description of the Bagger-Witten line bundle on a moduli space of Calabi-Yau's as a line bundle of covariantly constant spinors (resulting in a square root of the Hodge line bundle of holomorphic top-forms), (2) results suggesting that it (and the Hodge line bundle) is always flat, but possibly never trivial, over moduli spaces of Calabi-Yaus of maximal holonomy and dimension greater than two. We will propose its nontriviality as a new criterion for existence of UV completions of four-dimensional supergravity theories. If time permits, we will explicitly construct an example, to concretely display these properties, and outline results obtained with Ron Donagi and Mark Macerato for other cases.