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Register a new user$mathcal{N}=1$ supersymmetric three-dimensional QED in the large-$N_f$ limit and applications to super-graphene
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We study $mathcal{N}=1$ supersymmetric three-dimensional Quantum Electrodynamics with $N_f$ two-component fermions. Due to the infra-red (IR) softening of the photon, $ep$-scalar and photino propagators, the theory flows to an interacting fixed point deep in the IR, $p_E ll e^2 N_f/8$, where $p_E$ is the euclidean momentum and $e$ the electric charge. At next-to-leading order in the $1/N_f$-expansion, we find that the flow of the dimensionless effective coupling constant $overline{al}$ is such that: $overline{al} ra 8/big(N_f ,(1+C/N_f)big) approx (8/N_f)(1-0.4317/N_f)$ where $C= 2,(12-pi^2)/pi^2$. Hence, the non-trivial IR fixed point is stable with respect to quantum corrections. Various properties of the theory are explored and related via a mapping to the ones of a $mathcal{N}=1$ model of super-graphene. In particular, we derive the interaction correction coefficient to the optical conductivity of super-graphene, $C_{rm sg} = (12-pi^2)/(2pi) = 0.3391$, which is six times larger than in the non-supersymmetric case, $C_{rm g} = (92-9pi^2)/(18pi) = 0.0561$.
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We consider Quantum Electrodynamics in $2{+}1$ dimensions with $N_f$ fermionic or bosonic flavors, allowing for interactions that respect the global symmetry $U(N_f/2)^2$. There are four bosonic and four fermionic fixed points, which we analyze using the large $N_f$ expansion. We systematically compute, at order $O(1/N_f)$, the scaling dimensions of quadratic and quartic mesonic operators. We also consider Quantum Electrodynamics with minimal supersymmetry. In this case the large $N_f$ scaling dimensions, extrapolated at $N_f{=}2$, agree quite well with the scaling dimensions of a dual supersymmetric Gross-Neveu-Yukawa model. This provides a quantitative check of the conjectured duality.
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