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Highly Effective Actions

John H. Schwarz

(Submitted on 1 Nov 2013)

It is conjectured that the world-volume action of a probe D3-brane in an AdS_5 X S^5 background of type IIB superstring theory, with one unit of flux, can be reinterpreted as the exact effective action (or highly effective action) for U(2), N = 4 super Yang-Mills theory on the Coulomb branch. An analogous conjecture for U(2)_k X U(2)_{-k} ABJM theory is also presented. The main evidence supporting these conjectures is that the brane actions have all of the expected symmetries and dualities. Highly effective actions have general coordinate invariance, even though they describe nongravitational theories.

In the AdS/CFT paper that launched a thousand cites, Maldacena proposed an equivalence between three superconformal field theories, and three string-theory backgrounds of the form "AdS times something", with a stack of branes being the mediating concept. One is to think of a stack of branes as like an extended black hole, with the AdS space being the interior of the black hole, and the field theory being the quantum theory of the branes. The fluctuations in the field theory, are the fluctuations of the branes, and these create the AdS space around the branes, and all the objects that can exist in it. (The impressionism of this descriptions reflects the mostly intuitive nature of my own understanding of AdS/CFT. But I think it is broadly correct.)

However, Maldacena was able to specify the field theory only for one of his dualities - N=4 super-Yang-Mills (lately famous again, for having yet another description, as the amplituhedron), dual to strings in AdS5 x S5, the AdS space around a stack of D3-branes. Years later, in 2008, the field theory for another of these original dualities was found, this time for AdS4 x S7, the space around a stack of M2-branes. This theory is known as ABJM, after its four discoverers; the M is Maldacena himself.

But the nature of ABJM theory was anticipated years before, in a paper by John Schwarz, who proposed that the dual theory for M2-branes would be a Chern-Simons field coupled to matter. This was an impressive contribution for someone present at the creation of string theory, thirty years earlier. Schwarz was co-inventor of the "Neveu-Schwarz sector" of the superstring in the 1970s, he and Michael Green launched the 1980s string revolution with their discovery of the anomaly cancellation, and in the early 2000s, he managed to guess what the field dual of a stack of M2-branes would look like.

Now it's 2013 and he has presented what may be another inspired guess. That's why I'm hyping this paper a little, despite its very preliminary character, and despite the fact that I only have a slender grasp of its significance at this point. There seem to be two things to say about it. First, it's a refinement of the duality between field theory and strings in AdS space; Schwarz says that a particular form of the field theory - its "Coulomb branch" - corresponds to the presence of a particular brane in the AdS space. Second, Schwarz says that these ideas were motivated by an attempt to make progress with the third of Maldacena's original examples, the field theory corresponding to a stack of M5-branes. I don't see how that connection works yet, but I'll report any progress in understanding in this thread.

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# Schwarz actions for Maldacena branes

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