# Chiral indices and resolution independent structure in 4D F-theory vacua

I describe recent progress towards delineating the landscape of 4D F-theory flux vacua with chiral massless spectra. The main result of this effort is a novel, streamlined approach for computing vertical fluxes and 4D chiral indices that combines tools in intersection theory with the low energy effective description of F-theory geometry. A key feature of this approach is the vertical middle cohomology of smooth elliptic Calabi-Yau fourfolds resolving the singular F-theory limit, whose conjectural resolution independence offers deep insight into the geometric nature of the chiral indices. We illustrate the utility of this approach by analyzing vertical flux backgrounds for models with simple gauge groups, as well as models with a single abelian gauge factor; a notable example is the universal (SU(3) x SU(2) x U(1)) / Z_{6} model constructed in 1912.10991. In all cases we study, we find that vertical flux backgrounds can produce nontrivial chiral indices for all anomaly-free chiral matter spectra, suggesting that F-theory geometry imposes no additional linear constraints beyond those implied by anomaly cancellation.

## Department of Physics