Wilson Loops as Precursors

TL;DR

This paper explores how Wilson loops serve as non-local precursor operators in holographic theories, providing insight into how bulk events are encoded on the boundary before signals arrive.

Contribution

It demonstrates that Wilson loops, intrinsically non-local operators, can act as precursors in holographic duality, extending understanding beyond local gauge-invariant operators.

Findings

Wilson loops can encode bulk information before signals reach the boundary.

Precursor operators are necessarily non-local and cannot be constructed from local gauge-invariant operators.

The size of Wilson loops as precursors is determined by the UV-IR connection.

Abstract

There is substantial evidence that string theory on AdS_5 x S_5 is a holographic theory in which the number of degrees of freedom scales as the area of the boundary in Planck units. Precisely how the theory can describe bulk physics using only surface degrees of freedom is not well understood. A particularly paradoxical situation involves an event deep in the interior of the bulk space. The event must be recorded in the (Schroedinger Picture) state vector of the boundary theory long before a signal, such as a gravitational wave, can propagate from the event to the boundary. In a previous paper with Polchinski, we argued that the "precursor" operators which carry information stored in the wave during the time when it vanishes in a neighborhood of the boundary are necessarily non-local. In this paper we argue that the precursors cannot be products of local gauge invariant operators such as the energy momentum tensor. In fact gauge theories have a class of intrinsically non-local operators which cannot be built from local gauge invariant objects. These are the Wilson loops. We show that the precursors can be identified with Wilson loops whose spatial size is dictated by the UV-IR connection.