E-string quantum curve

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-...

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Autores principales:	Jin Chen, Babak Haghighat, Hee-Cheol Kim, Marcus Sperling, Xin Wang
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2021
Materias:	Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
Acceso en línea:	https://doaj.org/article/6d8a7fb4e1e94e51b5646df43d6eddf9
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id	oai:doaj.org-article:6d8a7fb4e1e94e51b5646df43d6eddf9
record_format	dspace
spelling	oai:doaj.org-article:6d8a7fb4e1e94e51b5646df43d6eddf92021-12-04T04:32:57ZE-string quantum curve0550-321310.1016/j.nuclphysb.2021.115602https://doaj.org/article/6d8a7fb4e1e94e51b5646df43d6eddf92021-12-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S0550321321002996https://doaj.org/toc/0550-3213In 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 SO(16) flavour symmetry in the UV, we find an enhancement in the IR to representations in terms of affine E8 characters. Finally, using the Nekrasov-Shatashvili limit of the E-string BPS partition function, we give a path integral derivation of the quantum curve.Jin ChenBabak HaghighatHee-Cheol KimMarcus SperlingXin WangElsevierarticleNuclear and particle physics. Atomic energy. RadioactivityQC770-798ENNuclear Physics B, Vol 973, Iss , Pp 115602- (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
spellingShingle	Nuclear and particle physics. Atomic energy. Radioactivity QC770-798 Jin Chen Babak Haghighat Hee-Cheol Kim Marcus Sperling Xin Wang E-string quantum curve
description	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 SO(16) flavour symmetry in the UV, we find an enhancement in the IR to representations in terms of affine E8 characters. Finally, using the Nekrasov-Shatashvili limit of the E-string BPS partition function, we give a path integral derivation of the quantum curve.
format	article
author	Jin Chen Babak Haghighat Hee-Cheol Kim Marcus Sperling Xin Wang
author_facet	Jin Chen Babak Haghighat Hee-Cheol Kim Marcus Sperling Xin Wang
author_sort	Jin Chen
title	E-string quantum curve
title_short	E-string quantum curve
title_full	E-string quantum curve
title_fullStr	E-string quantum curve
title_full_unstemmed	E-string quantum curve
title_sort	e-string quantum curve
publisher	Elsevier
publishDate	2021
url	https://doaj.org/article/6d8a7fb4e1e94e51b5646df43d6eddf9
work_keys_str_mv	AT jinchen estringquantumcurve AT babakhaghighat estringquantumcurve AT heecheolkim estringquantumcurve AT marcussperling estringquantumcurve AT xinwang estringquantumcurve
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E-string quantum curve

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