Entropy of Anisotropic Universe and Fractional Branes

TL;DR

This paper investigates the entropy of anisotropic universes with fractional branes, exploring conditions under which the expected entropy scaling is achieved and implications for the dimensionality of spacetime.

Contribution

It provides a detailed analysis of the entropy of fractional branes in anisotropic universes and links dualities and decay processes to the emergence of 3+1 dimensions.

Findings

Expected entropy forms are recovered under specific conditions.

T duality constrains high entropic configurations.

4 charge fractional branes may explain the dimensionality of our universe.

Abstract

We obtain the entropy of a homogeneous anisotropic universe applicable, by assumption, to the fractional branes in the universe in the model of Chowdhury and Mathur. The entropy for the 3 or 4 charge fractional branes thus obtained is not of the expected form E^{{3/2}} or E^2. One way the expected form is realised is if p \to \rho for the transverse directions and if the compact directions remain constant in size. These conditions are likely to be enforced by brane decay and annihilation, and by the S, T, U dualities. T duality is also likely to exclude high entropic cases, found in the examples, which arise due to the compact space contracting to zero size. Then the 4 charge fractional branes may indeed provide a detailed realisation of the maximum entropic principle we proposed recently to determine the number (3 + 1) of large spacetime dimensions.