Shan-Shan Xu University of Science and Technology of China Remarks on Dp & Dp−2 with each carrying a flux Interdisciplinary Center for Theoretical Study Based on J.X.Lu and S.S.Xu ’s work: arXiv: [hep-th]

Remarks on Dp & Dp−2 with each carrying a flux  Introduction Dp-brane,, bound states  Boundary state description  The string-level force calculations  The analysis of the amplitudes the long-range interactions the short distance behavior open string pair production  Summary

Introducion Dp-brane 1/2 BPS R-R charge super Yang-Mills a p-dimensional dynamical object on which open strings can end

Introducion One loop vacuum amplitudes are given by the Coleman-Weinberg formula, which can be thought of as the sum of the zero point energies of all the modes : no force conformal symmetry: NS-NSR-R the tree-level closed string cylinder diagram the open string one- loop annulus diagram Boundary state

Introduction bound state (p,q) F-string D string BPS bound: bound energy: almost the total tension of the F-string!

Introduction bound state: a Dp-brane with an electric flux, bound state: a Dp brane with one magnetic flux. a D0-brane and a Dp-brane The BPS bound: direct calculation of the interaction:

Boundary state The state that describes the creation of closed string from the vacuum is called the boundary state

Boundary state external flux on the world-volume

The string-level force calculation The interaction under consideration can be calculated as the vacuum amplitude of the closed string tree-level cylinder diagram via the closed string boundary states. the closed string propagator

The string-level force calculation the ghost contributions are independent of fluxes and are always given as To calculate and, make a respective unitary transformation of the oscillators in such that the -matrix there completely disappears while ends up with a new with Sp the original S-matrix in this boundary state and T denoting the transpose. This new S- matrix shares the same property as the original Sk satisfying with k = p−2 or p but its determinant is always unity and therefore can always be diagonalized to gives its eigenvalues.

The string-level force calculation the Class I matrix elements for matter fields are vacuum amplitude

The string-level force calculation the ClassII matrix elements for matter fields are vacuum amplitude: j=1,2

The string-level force calculation

the ClassIII matrix elements for matter fields are The string-level force calculation vacuum amplitude:

The analysis of the amplitudes the large-separation limit

The analysis of the amplitudes small separation the tree-level closed string cylinder diagram the open string one- loop annulus diagram divergenttachyon

The analysis of the amplitudes simple poles ： the rate of open string pair production per unit worldvolume in a constant electric flux in the present context is at least one electric flux (or being electrically dominant) along a NN-direction divergent enhancement factor

The analysis of the amplitudes divergenttachyon replusive interaction

The analysis of the amplitudes simple poles ： reduce the rate

The analysis of the amplitudes divergenttachyon BPS configuration:

The analysis of the amplitudes simple poles ： enhancement even

Summary The amplitudes of 17 flux configurations of Dp&Dp−2 3 structures of the expression the long-range interactionsone replusive force three BPS configurations open string pair production Further work and applications: tachyon condensation more than one flux low energy brane dynamics brane inflation To form a new bound state