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arXiv · 2103.16996

E-string Quantum Curve

Jin Chen·Babak Haghighat·Hee-Cheol Kim·Marcus Sperling·Xin Wang
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Abstract

In this work we study the quantisation of the Seiberg-Witten curve for the E-string theory compactified on a two-torus. We find that the resulting operator expression belongs to the class of elliptic quantum curves. It can be rephrased as an eigenvalue equation with eigenvectors corresponding to co-dimension 2 defect operators and eigenvalues to co-dimension 4 Wilson surfaces wrapping the elliptic curve, respectively. Moreover, the operator we find is a generalised version of the van Diejen operator arising in the study of elliptic integrable systems. Although the microscopic representation of the co-dimension 4 defect only furnishes an $\mathrm{SO}(16)$ flavour symmetry in the UV, we find an enhancement in the IR to representations in terms of affine $E_8$ characters. Finally, using the Nekrasov-Shatashvili limit of the E-string BPS partition function, we give a path integral derivation of the quantum curve.

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Jin Chen, Babak Haghighat, Hee-Cheol Kim, Marcus Sperling, Xin Wang. 2021-03-31. E-string Quantum Curve. https://doi.org/10.1016/j.nuclphysb.2021.115602

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