Time-periodicities in holographic CFTs

Abstract

Dynamics in AdS spacetimes is characterized by various time-periodicities. The most obvious of these is the time-periodic evolution of linearized fields, whose normal frequencies form integer-spaced ladders as a direct consequence of the structure of representations of the conformal group. There are also explicitly known time-periodic phenomena on much longer time scales inversely proportional to the coupling in the weakly nonlinear regime. We ask what would correspond to these long time periodicities in a holographic CFT, provided that such a CFT reproducing the AdS bulk dynamics in the large central charge limit has been found. The answer is a very large family of multiparticle operators whose conformal dimensions form simple ladders with spacing inversely proportional to the central charge. We give an explicit demonstration of these ideas in the context of a toy model holography involving a ϕ4 probe scalar field in AdS, but we expect the applicability of the underlying structure to be much more general.

Holographic solar systems and hydrogen atoms: non-relativistic physics in AdS and its CFT dual

“…There is a separate limit of non-relativistic classical fields in AdS (c → ∞, → 0, m → 0 with mω fixed), which is interesting but beyond the scope of this paper. The example of a self-gravitating free scalar field was studied in [25], and a field with quartic selfinteraction in [26]. These works illustrate our philosophy that many interesting problems in AdS have simpler non-relativistic analogues that nonetheless retain the salient features of the full problem.…”

Time-periodic quantum states of weakly interacting bosons in a harmonic trap

“…In such situations, one expects that ladders in the fine structure splitting, analogous to what we have seen for the LLL Hamiltonian, will emerge asymptotically in the fine structure of sufficiently high unperturbed energy levels. We intend to investigate some of these questions elsewhere [31]. in going from the second to the third line, and the Baker-Campbell-Hausdorff identity in going from the fourth to the fifth line.…”

Holographic quantum scars

“…On the gravity side, one can find various examples of periodic behavior ranging from studies of circular orbits in AdS black hole backgrounds [83] to discrete scale invariance [84,85], cyclic RG flows [86], "solar systems" in AdS and its CFT dual [87] or time-periodic behaviour of a probe self-interacting scalar field, exhibiting a tower-of-states like structure, on the AdS background [88]. See also [89][90][91][92] for related topics.…”