Four-Brane and Six-Brane Interactions in M(atrix) Theory

We discuss the proposed description of configurations with four-branes and six-branes in m(atrix) theory. Computing the velocity dependent potential between these configurations and gravitons and membranes, we show that they agree with the short distance string results computed in type IIa string theory. Due to the ``closeness'' of these configuration to a supersymmetric configuration the m(atrix) theory reproduces the correct long distance behavior.Comment: 14 pages, late

Lepton Masses and Mixing Angles with Spontaneously Broken O(3) Flavor Symmetry

We present a model based on an O(3) flavor symmetry and a minimal extension of the scalar sector to induce hierarchical breaking, O(3) -> O(2) -> SO(2) -> nothing. The model naturally accounts for all the known lepton parameters and yields various interesting predictions for others: (i) Neutrinos are nearly degenerate, m_\nu \sim 0.1 eV; (ii) The solar neutrino problem is solved by the MSW small mixing angle solution; (iii) The MNS mixing angle theta_{13} is unobservably small, theta_{13} = O(10^{-5}).Comment: 8 pages, LaTeX2e, published version, typos corrected and some of the notations were improve

Reexamination of entanglement of superpositions

We find tight lower and upper bounds on the entanglement of a superposition of two bipartite states in terms of the entanglement of the two states constituting the superposition. Our upper bound is dramatically tighter than the one presented in Phys. Rev. Lett 97, 100502 (2006) and our lower bound can be used to provide lower bounds on different measures of entanglement such as the entanglement of formation and the entanglement of subspaces. We also find that in the case in which the two states are one-sided orthogonal, the entanglement of the superposition state can be expressed explicitly in terms of the entanglement of the two states in the superposition.Comment: 5 pages, Published versio

Cut-off QFT and black hole entropy

We clarify the relationship between black hole entropy and the number of degrees of freedom in the dual QFT with a cut-off. We show that simple gravity arguments predict the correct cut-off procedure.Comment: 8 pages, Late