A note on CFT dual of RS model with gauge fields in bulk

TL;DR

The paper investigates the AdS/CFT dual of Randall-Sundrum models with gauge fields in the bulk, showing that a 4D CFT with a UV cut-off and gauged global symmetries provides a consistent dual description. A key result is that the Planck-brane gauge kinetic term $\tau_{UV}$ corresponds to a bare kinetic term for the CFT source, and the limit $\tau_{UV}\to0$ yields an induced gauge theory where CFT loops generate the kinetic term. The RS Planck-brane propagator, incorporating bulk and brane contributions, maps onto the CFT’s 1PI two-point function, with RS loop effects corresponding to sub-leading large-$N$ corrections in the CFT. Extending to RS1, the TeV brane signals conformal breaking and generates KK modes dual to CFT bound states; kinetic mixing between the external source and bound states explains the observed zero-mode profile and KK couplings to brane fields. Overall, the work provides a coherent framework linking RS bulk gauge dynamics to CFT data, highlighting both the calculable (external-scalar loops, large-$N$ limits) and the strongly coupled, model-dependent aspects of the dual description.

Abstract

It has been conjectured that the (weakly coupled) Randall-Sundrum (RS) model with gauge fields in the bulk is dual to a (strongly coupled) 4D conformal field theory (CFT) with an UV cut-off and in which global symmetries of the CFT are gauged. We elucidate features of this dual CFT which are crucial for a complete understanding of the proposed duality. We argue that the limit of no (or small) brane-localized kinetic term for bulk gauge field on the RS side (often studied in the literature) is dual to no bare kinetic term for the gauge field which is coupled to the CFT global current. In this limit, the kinetic term for this gauge field in the dual CFT is ``induced'' by CFT loops. Then, this CFT loop contribution to the gauge field 1PI two-point function is dual (on the RS side) to the full gauge propagator (i.e., including the contribution of Kaluza-Klein and zero-modes) with both external points on the Planck brane. We also emphasize that loop corrections to the gauge coupling on the RS side are dual to sub-leading effects in a large-N expansion on the CFT side; these sub-leading corrections to the gauge coupling in the dual CFT are (in general) sensitive to the strong dynamics of the CFT.