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Boundaries, Vermas and factorisation

Bullimore, Mathew; Crew, Samuel; Zhang, Daniel

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Samuel Crew

Daniel Zhang


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.


Bullimore, M., Crew, S., & Zhang, D. (2021). Boundaries, Vermas and factorisation. Journal of High Energy Physics, 2021(4), Article 263.

Journal Article Type Article
Acceptance Date Mar 29, 2021
Online Publication Date Apr 27, 2021
Publication Date 2021-04
Deposit Date Jul 28, 2021
Publicly Available Date Aug 23, 2021
Journal Journal of High Energy Physics
Print ISSN 1126-6708
Publisher Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed Peer Reviewed
Volume 2021
Issue 4
Article Number 263


Accepted Journal Article (706 Kb)

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Copyright 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.

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