Supersymmetric Graphene on Squashed Hemisphere

We compute the partition function of $\mathcal N=2$ supersymmetric mixed dimensional QED on a squashed hemisphere using localization. Mixed dimensional QED is an abelian gauge theory coupled to charged matter fields at the boundary. The partition function is a function of the complex gauge coupling $\tau$, the choice of R-symmetry and the squashing deformation. The superconformal R-symmetry is determined using the 3-dimensional F-maximization. The free energy as a function of squashing deformation allows computing correlation functions that contain the insertion of the energy-momentum tensor. We compute the 2-point correlation function of the boundary energy-momentum tensor by differentiating the free energy with respect to the squashing parameter. We comment on the behaviour of the 2-point function as we change the complex coupling $\tau$.