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Boundaries, Vermas and factorisation

Bullimore, Mathew and Crew, Samuel and Zhang, Daniel (2021) 'Boundaries, Vermas and factorisation.', Journal of High Energy Physics, 2021 (4). p. 263.


We revisit the factorisation of supersymmetric partition functions of 3d N = 4 gauge theories. The building blocks are hemisphere partition functions of a class of UV N = (2, 2) boundary conditions that mimic the presence of isolated vacua at infinity in the presence of real mass and FI parameters. These building blocks can be unambiguously defined and computed using supersymmetric localisation. We show that certain limits of these hemisphere partition functions coincide with characters of lowest weight Verma mod- ules over the quantised Higgs and Coulomb branch chiral rings. This leads to expressions for the superconformal index, twisted index and S3 partition function in terms of such characters. On the way we uncover new connections between boundary ’t Hooft anomalies, hemisphere partition functions and lowest weights of Verma modules.

Item Type:Article
Full text:(AM) Accepted Manuscript
Available under License - Creative Commons Attribution 4.0.
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Publisher statement:Open Access. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Date accepted:29 March 2021
Date deposited:28 July 2021
Date of first online publication:27 April 2021
Date first made open access:28 July 2021

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