Short-Distance Space-Time Structure and Black Holes in String Theory : A Short Review of the Present Status

TL;DR

This paper argues that a spacetime uncertainty principle, derived from world-sheet conformal symmetry, provides a universal, nonperturbative glimpse into the short-distance structure of string/M-theory and its black-hole physics. It develops detailed connections between D-brane dynamics, D-particle scattering, and matrix-model formulations (including Matrix theory and IKKT) to illustrate how minimal length scales and dualities emerge and how holography can be understood through UV/IR relations rooted in these uncertainties. The authors relate the principle to Maldacena’s AdS/CFT paradigm and to holographic bounds, suggesting generalized uncertainty relations in M-theory that underpin the holographic counting of degrees of freedom in bulk/boundary settings. Collectively, the work offers a coherent framework tying short-distance spacetime structure, nonperturbative definitions, and holographic principles, with concrete results for D-particles, D0-branes, and matrix-model descriptions of black holes.

Abstract

We briefly review the present status of string theory from the viewpoint of its implications on the short-distance space-time structure and black hole physics. Special emphases are given on two closely related issues in recent developments towards nonperturbative string theory, namely, the role of the space-time uncertainty relation as a qualitative but universal characterization of the short-distance structure of string theory and the microscopic formulation of black-hole entropies. We will also suggest that the space-time uncertainty relation can be an underlying principle for the holographic property of M theory, by showing that the space-time uncertainty relation naturally explains the UV/IR relation used in a recent derivation of the holographic bound for D3 brane by Susskind and Witten.