# Why isn't there heterotic holographic QCD?

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I think the question speaks for itself... Top-down holographic QCD, like Sakai-Sugimoto, always involves the Type II string. There are one or two papers on hQCD using the Type 0 string. But I can't see anyone making hQCD models using the heterotic string. Why not?

I may as well explain how the question arose: I was thinking about two forms of conventional string phenomenology - M-theory on G2 manifolds, and E8xE8 heterotic models - and was looking at possible beyond-standard-model symmetries, like flavor symmetries, family symmetries, etc. Somehow I stumbled into a time warp and ended up in 1965, looking at "The Covariant Theory of Strong Interaction Symmetries" by Salam, Delbourgo, and Strathdee, in which "A classification of particles is suggested based on a U(12) symmetry scheme". They want to make hadrons out of a "12-component (Dirac) quark" (i.e. u, d, s as a single "quark"), and propose representations for vector and pseudoscalar mesons, and spin 1/2 and spin 3/2 baryons. It occurred to me that it would be rather eccentric to think about ways to embed a variation of their scheme into E8xE8, but that someone working on holographic QCD might well be interested in forgotten approaches to the strong interactions; and yet, top-down hQCD employs Type II string theory, which is dual to the heterotic string. Why haven't insights from heterotic string theory played a role in holographic QCD so far?

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The utility of using branes to realize gauge theories in string theory, compared to using heterotic, lies in the ease with which we can decouple bulk gravity. Basically you can zoom in to the branes to isolate the degrees of freedom on them, forgetting the gravity.

In contrast, in heterotic compactificarions, both gauge fields and gravity live in the same 10d space, which makes it hard to separate them.

So, if the objective is to study e dynamics of gauge theory without gravity, using type II with branes is much more convenient.

Note that the gravity appearing in the holographic QCD is the gravity "very close" to the branes; the gravity degree of freedom I was referring to above was the gravity in the 10d bulk, not localized anywhere.

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answered Oct 9, 2011 by (1,390 points)

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