Towards bootstrapping \(QED_{3}\). (English) Zbl 1390.81498
Summary: We initiate the conformal bootstrap study of Quantum Electrodynamics in \(2+1\) space-time dimensions (\(QED_{3}\)) with \(N\) flavors of charged fermions by focusing on the 4-point function of four monopole operators with the lowest unit of topological charge. We obtain upper bounds on the scaling dimension of the doubly-charged monopole operator, with and without assuming other gaps in the operator spectrum. Intriguingly, we find a (gap-dependent) kink in these bounds that comes reasonably close to the large \(N\) extrapolation of the scaling dimensions of the singly-charged and doubly-charged monopole operators down to \(N = 4\) and \(N = 6\).
MSC:
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 83C50 | Electromagnetic fields in general relativity and gravitational theory |
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