Duality and Transport for Supersymmetric Graphene from the Hemisphere Partition Function

Abstract

We use localization to compute the partition function of a four dimensional, supersymmetric, abelian gauge theory on a hemisphere coupled to charged matter on the boundary. Our theory has eight real supercharges in the bulk of which four are broken by the presence of the boundary. The main result is that the partition function is identical to that of $\mathcal{N}=2$ abelian Chern-Simons theory on a three-sphere coupled to chiral multiplets, but where the quantized Chern-Simons level is replaced by an arbitrary complexified gauge coupling $\tau$. The localization reduces the path integral to a single ordinary integral over a real variable. This integral in turn allows us to calculate the scaling dimensions of certain protected operators and two-point functions of abelian symmetry currents at arbitrary values of $\tau$. Because the underlying theory has conformal symmetry, the current two-point functions tell us the zero temperature conductivity of the Lorentzian versions of these theories at any value of the coupling. We comment on S-dualities which relate different theories of supersymmetric graphene. We identify a couple of self-dual theories for which the complexified conductivity associated to the U(1) gauge symmetry is $\tau /2$.

arXiv comment36 pages, 6 figures; v2 refs added

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• Holographic and Localization Calculations of Boundary F for $\mathcal{N}=4$ SUSY Yang-Mills Theory
• Conformal Surface Defects in Maxwell Theory are Trivial
• Janus interface entropy and Calabi's diastasis in four-dimensional $\mathcal{N}=2$ superconformal field theories
• Supersymmetric Graphene on Squashed Hemisphere
• Solving $\mathcal{N}=4$ SYM BCFT matrix models at large $N$
• Critical properties of three-dimensional many-flavour QEDs
• One-point functions for doubly-holographic BCFTs and backreacting defects
• Two-loop mass anomalous dimension in reduced quantum electrodynamics and application to dynamical fermion mass generation
• Perturbative aspects of the supersymmetric three-dimensional massive QED