E‐String Theory on Riemann Surfaces

We study compactifications of the 6d E‐string theory, the theory of a small E8 instanton, to four dimensions. In particular we identify field theories in four dimensions corresponding to compactifications on arbitrary Riemann surfaces with punctures and with arbitrary non‐abelian flat connections as well as fluxes for the abelian sub‐groups of the E8 flavor symmetry. This sheds light on emergent symmetries in a number of 4d SCFTs (including the ‘E7 surprise’ theory) as well as leads to new predictions for a large number of 4‐dimensional exceptional dualities and symmetries.