Past exam of the mathematics course of the University of Cambridge / 2001 / iii / Paper 66 / 1 / c

A supersymmetric type-II D-brane carries a Ramond–Ramond potential charge and saturates the corresponding generalized BPS bound in supersymmetry: its brane tension equals the charge-dependent central/tensorial-charge bound in the relevant normalization. It is therefore a BPS state, preserving sixteen of the thirty-two spacetime supercharges. Identical parallel branes with the same orientation impose the same supersymmetry projector. This statement does not apply to arbitrary unstable non-BPS branes or to the bosonic branes of the preceding parts.

One direct demonstration of the parallel D-brane no-force identity is the annulus vacuum amplitude. For separation $r$, its oscillator-dependent part is proportional toHereThe first two terms describe the projected Neveu–Schwarz sector, and the last is the oppositely signed Ramond sector contribution. The Jacobi abstruse identity gives $f_3^8-f_4^8-f_2^8=0$ for every $t$. ThereforeIn the closed-string channel, attractive graviton and dilaton exchange cancel repulsive Ramond–Ramond potential exchange. The classical probe calculation in the D-brane supergravity solution gives the same cancellation. The common supersymmetry allows separation to remain a flat modulus; relative angles, reversed RR charge or supersymmetry-breaking backgrounds can remove this protection. For a brane–antibrane pair the RR interaction reverses and does not cancel the NS-NS attraction. The charge and half-supersymmetry interpretation is established in Dirichlet-Branes and Ramond-Ramond Charges.