Holography in the Flat Space Limit

TL;DR

The paper investigates how holography encodes bulk physics in lower-dimensional theories, focusing on the flat-space limit of matrix theory and AdS/CFT. It argues that the holographic mapping becomes increasingly nonlocal as N grows, with the flat-space limit realized by letting N→∞ at fixed coupling, and highlights the IR-UV connection that ties boundary degrees of freedom to bulk locality. Through analysis of D0-branes, D-instantons, and the role of high-frequency boundary modes, it shows that bulk information is distributed across many degrees of freedom in a nontrivial, highly nonlocal manner. The work also discusses potential strategies for decoding the hologram and outlines the challenges in extracting concrete flat-space amplitudes from holographic data, while emphasizing the deep connections between holography, matrix quantum mechanics, and nonperturbative string theory.

Abstract

Matrix theory and the AdS/CFT correspondence provide nonperturbative holographic formulations of string theory. In both cases the finite N theories can be thought of as infrared regulated versions of flat space string theory in which removing the cutoff is equivalent to letting N go to infinity. In this paper we consider the nature of this limit. In both cases the holographic mapping becomes completely nonlocal. In matrix theory this corresponds to the growth of D0-brane bound states with N. For the AdS/CFT correspondence there is a similar delocalization of the holographic image of a system as N increases. In this case the limiting theory seems to require a number of degrees of freedom comparable to large N matrix quantum mechanics.