Brane Couplings from Bulk Loops

TL;DR

This work analyzes loop corrections in a five-dimensional Yukawa theory on the orbifold $S_1/Z_2$ and shows that bulk loop divergences must be absorbed by brane-localized operators at the fixed points $x_5=0$ and $x_5=L$, implying a bulk-to-brane renormalization group running. The authors develop an orbifold propagator formalism and compute fermion and scalar loops, identifying brane terms such as a brane-localized fermion kinetic operator with a running coefficient proportional to $log(mu/M)$ and, for scalars, a brane operator involving derivatives in the fifth dimension ($partial_5^3 phi$), with higher-derivative brane operators expected at higher loops. They also show that certain brane renormalizations, like the brane Yukawa coupling, do not diverge at one loop. Overall, the results demonstrate that orbifold field theories intrinsically couple bulk dynamics to brane physics through renormalization group flow, with important implications for extra-dimensional model building.

Abstract

We compute loop corrections to the effective action of a field theory on a five-dimensional $S_1/Z_2$ orbifold. We find that the quantum loop effects of interactions in the bulk produce infinite contributions that require renormalization by four-dimensional couplings on the orbifold fixed planes. Thus bulk couplings give rise to renormalization group running of brane couplings.

Figures (7)

• Figure 1: One loop correction to the fermion propagator.
• Figure 2: One loop contribution to the scalar tadpole.
• Figure 3: One loop correction to the scalar propagator.
• Figure 4: Two loop correction to the scalar propagator.
• Figure 5: The association of the $\eta$s with the propagators in figure \ref{['fig-4']}.