Supersymmetric ground states of 3d $mathcal{N}=4$ SUSY gauge theories and Heisenberg algebras

Supersymmetric ground states of 3d $mathcal{N}=4$ SUSY gauge theories and Heisenberg algebras

Blog Article

We consider 3d $mathcal{N}=4$ theories on the geometry $Sigma imes mathbb{R}$, where $Sigma$ is a closed and connected Riemann surface, from the point of view of a quantum mechanics on Wooden Toy $mathbb{R}$.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 Scales 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.