Boundaries, Vermas and factorisation

Bullimore, Mathew; Crew, Samuel; Zhang, Daniel

Abstract

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.

Citation

Bullimore, M., Crew, S., & Zhang, D. (2021). Boundaries, Vermas and factorisation. Journal of High Energy Physics, 2021(4), Article 263. https://doi.org/10.1007/jhep04%282021%29263

• 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
• DOI: https://doi.org/10.1007/jhep04%282021%29263