E-string quantum curve

In this work we study the quantisation of Seiberg-Witten curve for E-string theory compactified on a two-torus. We find that resulting operator expression belongs to class elliptic quantum curves. It can be rephrased as an eigenvalue equation with eigenvectors corresponding co-dimension 2 defect operators and eigenvalues 4 Wilson surfaces wrapping curve, respectively. Moreover, is generalised version van Diejen arising in integrable systems. Although microscopic representation only furnishes SO(16) flavour symmetry UV, enhancement IR representations terms affine E8 characters. Finally, using Nekrasov-Shatashvili limit BPS partition function, give path integral derivation curve.