Remarks on Dp & Dp−2 with each carrying a flux

1. Remarks on Dp & Dp−2 with each carrying a flux Shan-Shan Xu Interdisciplinary Center for Theoretical Study University of Science and Technology of China Based on J.X.Lu and S.S.Xu ’s work: arXiv: 0906.0679 [hep-th]

2. 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

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

4. 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 NS-NS R-R conformal symmetry: the open string one-loop annulus diagram the tree-level closed string cylinder diagram Boundary state

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

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

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

8. Boundary state external flux on the world-volume

9. 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

10. 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.

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

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

14. The string-level force calculation

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

16. The analysis of the amplitudes the large-separation limit

17. The analysis of the amplitudes small separation the tree-level closed string cylinder diagram the open string one-loop annulus diagram divergent tachyon

18. 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

19. The analysis of the amplitudes divergent tachyon replusive interaction

20. The analysis of the amplitudes simple poles： reduce the rate

21. The analysis of the amplitudes divergent tachyon BPS configuration:

22. The analysis of the amplitudes simple poles： enhancement even

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