Abstract
We consider quantum field theory in a five-dimensional anti-de Sitter background, possibly truncated by four-dimensional (4D) branes. In the Euclidian version of this space, it is known that propagators exponentially decay when they go far enough toward the Poincar\'e horizon, i.e. deep enough into the IR region of the AdS bulk. In this note, we show that an analogous property exists in Lorentzian AdS. The exponential suppression is found to occur in the presence of bulk interactions dressing the AdS propagators. We calculate one-loop gravitational dressing and find that the suppression effect comes from the scalar component of the 5D graviton. We then argue that, at least at strong coupling, this exponential decay censors the region of spacetime where the 5D effective field theory would become invalid. As an application we estimate the rate for the cascade decay of bulk fields---which are known to produce soft spherical events with high multiplicity---and find this rate to be exponentially suppressed.
Highlights
Quantum field theory in anti de-Sitter spacetime has been a source of deep formal insights as well as elegant phenomenological developments for at least two decades
We have found that opacity of Lorentzian AdS is a consequence of bulk interactions and happens essentially because Kaluza Klein (KK) modes can decay into lighter KK modes
We have shown that propagators in a truncated Lorentzian AdS5 background are exponentially suppressed in the IR region of the bulk when the conformal pco1⁄4ordpinffipaffiffitffiμeffipffiffiffiμffiffiz
Summary
Quantum field theory in anti de-Sitter spacetime has been a source of deep formal insights as well as elegant phenomenological developments for at least two decades. This essential fact as long been known (see, e.g., [4,5]), and it is perhaps in [6] that it has been made clear that the position-dependent cutoff results from the presence of higher dimensional operators in the effective 5D theory Another feature inherent to curved space, known in the Euclidian version of AdS, is that propagators become exponentially suppressed when one of the end points in the fifth dimension goes too far in the IR. Since the position-dependent cutoff is present in Lorentzian AdS, one may wonder if a similar mechanism of “censorship” of the IR region may happen, which would require a decay of the propagator in the IR as in the Euclidian case. The scalar bulk mass has to satisfy the Breitenlohner-Freedman bound m2Φ ≥ −4k2 to prevent tachyonic instabilities in AdS5 [8]
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