Entropy of Anisotropic Universe and Fractional Branes

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. The expected form is realised if p → ρ 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.