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I've been brushing up on my string theory using Becker, Becker, Schwarz (p. 208 in particular). They state that some D-branes can couple to R-R fields from closed string excitations.

They then go on to say that these branes are exactly 1/2 BPS and therefore stable. I understand that 1/2 BPS objects are stable because they preserve enough of the supersymmetry.

But I don't understand why the coupling to R-R fields ensures that the branes are 1/2 BPS.

Could someone possibly explain this point mathematically, and/or direct me to a reference that makes it clear?

Many thanks for your help!

Edit: perhaps the answer is contained within Polchinski's seminal paper here? Still might be useful to get a second opinion!

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