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Quantized Coulomb branches, monopole bubbling and wall-crossing phenomena in 3d N=4 theories.

Assel, Benjamin and Cremonesi, Stefano and Renwick, Matthew (2020) 'Quantized Coulomb branches, monopole bubbling and wall-crossing phenomena in 3d N=4 theories.', Journal of high energy physics., 2020 (4). p. 213.


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.

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Publisher statement: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:11 April 2020
Date deposited:07 May 2020
Date of first online publication:30 April 2020
Date first made open access:07 May 2020

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