# Are magnetic charges compulsory in string theory?

In this penultimate lecture of a series given by Freddy Cachazo, the differential forms corresponding to the massless excitations in the Ramond–Ramond sector signal the existence of p-branes sourcing the associated fields. We find 0- and 2-branes for the type II-A case, and (-1)-, 1- and 3-branes for the type II-B case.

However, for some reason that I didn't follow, we also assume that there also exist "magnetically" charged branes dual to the "electrically" charged ones, yielding the additional 6- and 4-branes for type II-A, and the 7- and 5-branes for type II-B (the dual to the 3-brane is also a 3-brane). We also get an NS5-brane dual to the fundamental string in the NS-NS sector.

Why are these additional objects said to exist? Is it a self-consistency condition, or simply an explicit assumption?

If it's the former, does the same apply for the bosonic theory, i.e. would it need an NS21-brane dual to the fundamental string to be self-consistent?

The "charged branes" in superstring theory arise from the democratic formulation of the Ramond-Ramond fields, where to each "naive" Ramond potential $$C_p$$ (the "electric" potential) there is a dual potential $$C_{8-p}$$ (the "magnetic" potential) and the two are on-shell related by their field strengths being duals of each other: $$\mathrm{d}C_{p} = {\star}\mathrm{d}C_{8-p}$$ The names "magnetic" and "electric" arise because this is a generalization of classical electromagnetic duality in vacuum, see e.g. this answer of mine.
All of these RR fields can have source terms, just like electric current in classical EM: $$\mathrm{d}{\star}\mathrm{d}C_p = {\star}J_{p}$$, where the current is a $$p$$-form, meaning it gives charge when integrated over a subvolume with $$p$$ dimensions, which can be interpreted as the worldvolumes of $$p-1$$-branes, so its "charged objects" are $$p-1$$-branes. This is exactly analogous to ordinary electric current being a 1-form because it is sourced by the worldlines of particles (=0-branes). Again the "electric"/"magnetic" terminology arises because the $$C_p$$-charged branes are electric and the $$C_{8-p}$$-charged branes are magnetic.
• @turbodiesel4598 it is exactly the same logic: The string is a 1-brane, so it is charged under some $C_2$, the dual of that is a $C_6$, and the charged objects of that are 5-branes. The field under which it is charged is just the Kalb-Ramond field instead of one of the RR fields. Oct 18, 2022 at 15:05