D-branes, Black Holes and $SU(\infty)$ Gauge Theory

TL;DR

This paper explores the application of large N gauge theory to string theory and black holes, proposing that quantum black holes follow infinite statistics and connecting motives and L-functions to fundamental physics issues.

Contribution

It introduces a novel link between $SU( Infinity)$ gauge theory, black hole statistics, and motives, proposing a new framework for string and p-brane theories.

Findings

Black holes obey infinite (Boltzmann) statistics.

Partition functions relate to L-functions of motives.

Connections between motives, L-functions, and the cosmological constant.

Abstract

We discuss an application of the known in QCD large $N$ expansion to strings and supermembranes in the strong coupling. In particular we use the recently obtained master field describing $ SU(\infty)$ gauge theory to argue that quantum extreme black holes obey quantum Boltzmann (infinite) statistics. This supports a topological argument by Strominger that black holes obey infinite statistics. We also speculate on a formulation of $X$-theory of strings and p-branes as theory of Grothendieck's motives. The partition function is expressed in terms of $L$-function of a motive. The Beilinson conjectures on the values of $L$-functions are interpreted as dealing with the cosmological constant problem.