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

TL;DR

This paper explores the duality between the Randall-Sundrum model with bulk gauge fields and a 4D conformal field theory with a UV cutoff, clarifying how gauge dynamics and loop effects correspond across the duality.

Contribution

It clarifies the duality between RS models with gauge fields and CFTs, especially regarding kinetic terms and loop corrections, enhancing understanding of gauge field dualities.

Findings

Kinetic terms in the dual CFT are induced by CFT loops.

Loop corrections in RS correspond to sub-leading effects in large-N CFT.

Duality details depend on brane-localized kinetic term limits.

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.