TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.16.4.090
TI  - Conformal boundary conditions for a 4d scalar field
PY  - 2024/04/03
UR  - https://scipost.org/SciPostPhys.16.4.090
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 16
IS  - 4
SP  - 090
A1  - Di Pietro, Lorenzo
AU  - Lauria, Edoardo
AU  - Niro, Pierluigi
AB  - 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 $k≠ 0$. 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.
ER  -

@Article{10.21468/SciPostPhys.16.4.090,
	title={{Conformal boundary conditions for a 4d scalar field}},
	author={Lorenzo Di Pietro and Edoardo Lauria and Pierluigi Niro},
	journal={SciPost Phys.},
	volume={16},
	pages={090},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.16.4.090},
	url={https://scipost.org/10.21468/SciPostPhys.16.4.090},
}