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I'm trying to understand the elements of the AdS-CFT correspondence. The definition I have in mind is a correspondence between:

  • (A) a Super String Theory of $D_p$-branes and closed strings in a $10$d flat bulk, with open strings living on the branes
  • (B) a $II$B Supergravity Theory where closed strings live in a $10$d bulk that is asymptotically flat and tends to $AdS_5 \times S^5$ near the origin

and the two are linked because the curved spacetime of theory (B) is the effect that the $D_p$-branes of theory (A) would have on a flat spacetime. Then if one chooses $p=3$ fun things happen in the low-energy limit.
My question is, why is (A) called a SST and (B) is called a SUGRA? I mean, they both have closed strings. Is the only difference between the two theories (in general, not necessarily applied to the AdS-CFT correspondence) the absence of open strings in SUGRA?

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    $\begingroup$ Well Type IIA and IIB supergravity are low-energy effective actions of the respective string theories, and conversely the string theories are supposedly their UV completions. I don't think there are "strings" in SUGRA as such. $\endgroup$ – Nihar Karve May 18 at 10:21
  • $\begingroup$ @NiharKarve I did not have in mind the clear concept of SUGRA being the low-energy effective theory of SST, but this makes perfect sense: closed strings are decoupled in (A), so they are in (B) also, therefore the SUGRA of (B) is the low-energy theory of the open+brane sector of (A). $\endgroup$ – Mauro Giliberti May 18 at 10:49

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