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Conformal boundary conditions for a 4d scalar field
by Lorenzo Di Pietro, Edoardo Lauria, Pierluigi Niro
This Submission thread is now published as
Submission summary
| Ontological classification |
|---|
| Academic field: |
Physics |
| Specialties: |
- High-Energy Physics - Theory
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| Approach: |
Theoretical |
Abstract
We construct unitary, stable, and interacting conformal boundary conditions for a free massless scalar in four dimensions by coupling it to edge modes living on a boundary. The boundary theories we consider are bosonic and fermionic QED$_3$ with $N_f$ flavors and a Chern-Simons term at level $k$, in the large-$N_f$ limit with fixed $k/N_f$. We find that interacting boundary conditions only exist when $k\neq 0$. To obtain this result we compute the $\beta$ functions of the classically marginal couplings at the first non-vanishing order in the large-$N_f$ expansion, and to all orders in $k/N_f$ and in the couplings. To check vacuum stability we also compute the large-$N_f$ effective potential. We compare our results with the the known conformal bootstrap bounds.
