TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.14.4.063
TI  - Supersymmetric ground states of 3d $\mathcal{N}=4$ SUSY gauge theories and Heisenberg algebras
PY  - 2023/04/06
UR  - https://scipost.org/SciPostPhys.14.4.063
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 14
IS  - 4
SP  - 063
A1  - Ferrari, Andrea E. V.
AB  - We consider 3d $\mathcal{N}=4$ theories on the geometry $\Sigma \times \mathbb{R}$, where $\Sigma$ is a closed and connected Riemann surface, from the point of view of a quantum mechanics on $\mathbb{R}$. Focussing on the elementary mirror pair in the presence of real deformation parameters, namely SQED with one hypermultiplet (SQED[1]) and the free hypermulitplet, we study the algebras of local operators in the respective quantum mechanics as well as their action on the vector space of supersymmetric ground states. We demonstrate that the algebras can be described in terms of Heisenberg algebras, and that they act in a way reminiscent of Segal-Bargmann (B-twist of the free hypermultiplet) and Nakajima (A-twist of SQED[1]) operators.
ER  -

@Article{10.21468/SciPostPhys.14.4.063,
	title={{Supersymmetric ground states of 3d $\mathcal{N}=4$ SUSY gauge theories and Heisenberg algebras}},
	author={Andrea E. V. Ferrari},
	journal={SciPost Phys.},
	volume={14},
	pages={063},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.14.4.063},
	url={https://scipost.org/10.21468/SciPostPhys.14.4.063},
}