Opacity from Loops in AdS

Abstract

We investigate how quantum dynamics affects the propagation of a scalar field in Lorentzian AdS. We work in momentum space, in which the propagator admits two spectral representations (denoted “conformal” and “momentum”) in addition to a closed-form one, and all have a simple split structure. Focusing on scalar bubbles, we compute the imaginary part of the self-energy ImΠ in the three representations, which involves the evaluation of seemingly very different objects. We explicitly prove their equivalence in any dimension, and derive some elementary and asymptotic properties of ImΠ.Using a WKB-like approach in the timelike region, we evaluate the propagator dressed with the imaginary part of the self-energy. We find that the dressing from loops exponentially dampens the propagator when one of the endpoints is in the IR region, rendering this region opaque to propagation. This suppression may have implications for field-theoretical model-building in AdS. We argue that in the effective theory (EFT) paradigm, opacity of the IR region induced by higher dimensional operators censors the region of EFT breakdown. This confirms earlier expectations from the literature. Specializing to AdS5, we determine a universal contribution to opacity from gravity.

On duality of color and kinematics in (A)dS momentum space

“…It would be interesting to study these theories in AdS and see if color-kinematics can be understood at the Lagrangian level. Finally, there has been progress in computing loop level AdS correlators through bulk and boundary unitarity methods [31,[82][83][84][85][86][87]. 13 In flat space, generalized unitarity and double-copy relations can be systematically used to study higher-loop graviton amplitudes…”

Loops in AdS: from the spectral representation to position space. Part II

“…Other computations rely on the conformal symmetry or the supersymmetry of the dual theory [41][42][43][44][45][46][47][48][49][50][51][52][53][54]. For additional works on AdS amplitudes and in particular loop amplitudes, see [55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71].…”

Four-point correlation modular bootstrap for OPE densities

“…Although we do not directly explore a gravitational interpretation of our work, we expect it to provide a reliable semi-classical description of AdS 3 gravity even at finite values of c [22,46]. Along the same lines, it would be interesting to derive some of the results of this paper from a purely gravitational analysis, in particular through the computation of the Witten diagrams corresponding to the four-point function of scalars considered here, by using several of the methods developed recently [47][48][49][50][51]. Our results will be useful for studies of coarse-graining CFTs to produce gravitational duals, along the lines of [19,22,25,52,53].…”