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String theory false vacua can be described by effective Lagrangians at low energy. Is there generally a correspondence between these effective Lagrangians and SU(N) gauge theories? Or do the effective Lagrangians often not respect local invariance with respect to some or any gauge groups?

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In $d=4$, there must be pretty much always a gauge group in the spectrum. It's not a theorem but there's strong evidence for it. Note that to find a gauge group, it's enough to find any spin-one light string excitation. A Yang-Mills symmetry must exist to render its negative-norm time-like polarization harmless - in fact, one may explicitly show by stringy methods that the gauge symmetry is there in any formalism that is Lorentz-covariant. The spin-1 fields arise either from the 10D gauge group e.g. in braneworlds or heterotic strings or from the RR fields or B-fields wrapped on cycles. –  LuboŇ° Motl Mar 26 '13 at 8:59
@LuboŇ° Motl -- Great, thanks! Do you know of any references (or key words to search for) that I could look up? –  user1247 Mar 26 '13 at 9:03

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