Quantized Coulomb Branches, Monopole Bubbling and Wall-Crossing Phenomena in 3d N=4 Theories

Assel, Benjamin; Cremonesi, Stefano; Renwick, Matthew

Abstract

To study the quantized Coulomb branch of 3d N = 4 unitary SQCD theories, we propose a new method to compute correlators of monopole and Casimir operators that are inserted in the R×R2ε Omega background. This method combines results from supersymmetric localization with inputs from the brane realisation of the correlators in type IIB string theory. The main challenge is the computation of the partition functions of certain Super-Matrix-Models (SMMs), which appear in the contribution of monopole bubbling sectors and are realised as the theory living on the D1 strings in the brane construction. We find that the non-commutativity arising in the monopole operator insertions is related to a wall-crossing phenomenon in the FI parameter space of the SMM. We illustrate our method in various examples and we provide explicit results for arbitrary correlators of non-bubbling bare monopole operators. We also discuss the realisation of the non-commutative product as a Moyal (star) product and use it to successfully test our results.

Citation

Assel, B., Cremonesi, S., & Renwick, M. (2020). Quantized Coulomb Branches, Monopole Bubbling and Wall-Crossing Phenomena in 3d N=4 Theories. Journal of High Energy Physics, 2020(4), Article 213. https://doi.org/10.1007/jhep04%282020%29213

• Journal Article Type: Article
• Acceptance Date: Apr 11, 2020
• Online Publication Date: Apr 30, 2020
• Publication Date: Apr 30, 2020
• Deposit Date: Oct 7, 2019
• Publicly Available Date: May 7, 2020
• Journal: Journal of High Energy Physics
• Print ISSN: 1126-6708
• Electronic ISSN: 1029-8479
• Publisher: Scuola Internazionale Superiore di Studi Avanzati (SISSA)
• Peer Reviewed: Peer Reviewed
• Volume: 2020
• Issue: 4
• Article Number: 213
• DOI: https://doi.org/10.1007/jhep04%282020%29213
• Public URL: https://durham-repository.worktribe.com/output/1319396
• Publisher URL: https://link.springer.com/article/10.1007/JHEP04(2020)213
• Related Public URLs: https://arxiv.org/abs/1910.01650