Toward a Theory of Precursors

TL;DR

The paper investigates how bulk locality may fail in AdS/CFT and seeks boundary observables, termed precursors, that encode interior bulk information. It introduces a concrete toy model in which a bulk dilaton wave maps to a boundary squeezed state, showing that nonlocal boundary observables can detect bulk excitations before they reach the boundary, in line with the UV/IR relation. The authors argue that Wilson loops, particularly decorated loops, are natural candidates for precursors in the gauge theory, though a complete identification requires a full string-theoretic treatment beyond the free-field approximation. Overall, the work clarifies how holography might realize bulk nonlocality through boundary probes and points to future string-theory analyses to fully decode the hologram.

Abstract

To better understand the possible breakdown of locality in quantum gravitational systems, we pursue the identity of precursors in the context of AdS/CFT. Holography implies a breakdown of standard bulk locality which we expect to occur only at extremely high energy. We consider precursors that encode bulk information causally disconnected from the boundary and whose measurement involves nonlocal bulk processes. We construct a toy model of holography which encapsulates the expected properties of precursors and compare it with previous such discussions. If these precursors can be identified in the gauge theory, they are almost certainly Wilson loops, perhaps with decorations, but the relevant information is encoded in the high-energy sector of the theory and should not be observable by low energy measurements. This would be in accord with the locality bound, which serves as a criterion for situations where breakdown of bulk locality is expected.

Figures (4)

• Figure 1: A point-like dilaton source at $\tau=0$ creates an outgoing wave which reaches the boundary at $\tau = \pi/2$ and then reflects back toward the interior.
• Figure 2: The size of the precursor with non-zero expectation value decreases as the dilaton wavefront approaches the boundary in accordance with the UV/IR relation.
• Figure 3: A Wilson loop $W[C]$ in the boundary theory with UV cutoff $\delta$ corresponds in the bulk to a string field operator $\Phi[\rho=\pi/2-\delta, C]$.
• Figure 4: A decorated Wilson loop corresponds in the bulk to a world sheet with vertex operators at the locations of the decorations.