Modularity of (rational) flux vacua
Shamit Kachru (Stanford)
Title: Modularity of (rational) flux vacua
Abstract: Compactifications of type IIb string theory on Calabi-Yau threefolds admit choices of background three-form fluxes, specified by selecting pairs of integral 3-forms on the manifold. In the presence of such fluxes, special points in the moduli space of complex structures on the Calabi-Yau emerge as (energetically) preferred by the physics. In this talk, we describe a happy coincidence: the manifolds which are preferred, in the case the Calabi-Yau is rational, are precisely those whose associated point counts yield weight-2 cusp forms in accord with certain modularity conjectures. These weight-2 forms naturally hint at the presence of a hidden elliptic curve in the physics and geometry, and we show that a physics construction (known as the "F-theory lift" of the model) makes the presence of the hidden elliptic curve manifest.
Recording taken from the Arithmetic Geometry and Quantum Field Theory seminar, organised by Jeff Harvey and Minhyong Kim