  We perform a comprehensive study of charged lepton flavour violation in
Randall-Sundrum (RS) models in a fully 5D quantum-field-theoretical framework.
We consider the RS model with minimal field content and a "custodially
protected" extension as well as three implementations of the IR-brane localized
Higgs field, including the non-decoupling effect of the Kaluza-Klein (KK)
excitations of a narrow bulk Higgs. Our calculation provides the first complete
result for the flavour-violating electromagnetic dipole operator in
Randall-Sundrum models. It contains three contributions with different
dependence on the magnitude of the anarchic 5D Yukawa matrix, which can all be
important in certain parameter regions. We study the typical range for the
branching fractions of mu -> e gamma, mu -> 3e, mu N -> e N as well as tau ->
mu gamma, tau -> 3 mu and the electron electric dipole moment by a numerical
scan in both the minimal and the custodial RS model. The combination of mu -> e
gamma and mu N -> e N currently provides the most stringent constraint on the
parameter space of the model. A typical lower limit on the KK scale T is around
2 TeV in the minimal model (up to 4 TeV in the bulk Higgs case with large
Yukawa couplings), and around 4 TeV in the custodially protected model, which
corresponds to a mass of about 10 TeV for the first KK excitations, far beyond
the lower limit from the non-observation of direct production at the LHC.
