The long-range interactions between branes in diverse dimensions

We calculate the long-range interactions between two simple branes placed parallel at a separation in diverse dimensions via an effective field theory approach. We also compute for the first time the explicit long-range interaction between two D-branes with each carrying a world-volume non-abelian magnetic flux in three special cases, respectively. In particular, we demonstrate that the half-string creation between a D$_0$-brane and a D$_8$-brane continues to hold even in the present context, therefore lending further support to the previous assertion of this. Our computations re-raise also the issue in one case on whether so constructed (D$_0$, D$_8$) bound state is actually a marginal one.Comment: 28 pages, various discussions expanded and references adde

A note on the fractional Cauchy problems with nonlocal initial conditions

AbstractOf concern is the Cauchy problems for fractional integro-differential equations with nonlocal initial conditions. Using a new strategy in terms of the compactness of the semigroup generated by the operator in the linear part and approximating technique, a new existence theorem for mild solutions is established. An application to a fractional partial integro-differential equation with a nonlocal initial condition is also considered