Superconformal Models for Graphene and Boundary Central Charges

TL;DR

This paper explores supersymmetric boundary conformal field theories inspired by graphene, demonstrating that boundary central charges depend on marginal couplings and are not renormalized, with potential exceptions in maximally supersymmetric cases.

Contribution

It introduces supersymmetric models with boundary conditions in various supercharge settings, showing boundary central charges depend on coupling and are not renormalized at all orders.

Findings

Boundary central charges depend on the gauge coupling.

Gauge coupling remains unrenormalized at all orders.

Difference between boundary charges may be coupling independent in maximally supersymmetric case.

Abstract

In the context of boundary conformal field theory, we investigate whether the boundary trace anomaly can depend on marginal directions in the presence of supersymmetry. Recently, it was found that a graphene-like non-supersymmetric conformal field theory with a four-dimensional bulk photon and a three-dimensional boundary electron has two boundary central charges that depend on an exactly marginal direction, namely the gauge coupling. In this work, we supersymmetrize this theory, paying special attention to the boundary terms required by supersymmetry. We study models with 4, 8, and 16 Poincar\'e supercharges in the bulk, half of which are broken by the boundary. In all cases, we find that at all orders in perturbation theory, the gauge coupling is not renormalized, providing strong evidence that these theories are boundary conformal field theories. Moreover, the boundary central charges depend on the coupling. One possible exception to this dependence on marginal directions is that the difference between the two charges is coupling independent at one-loop in the maximally supersymmetric case. In our analysis, a possible boundary Chern-Simons term is incorporated by a bulk $\theta$-term.