Quote by marcus
String experts have decided after several decades experience that one should NOT think in terms of strings and branes in a geometry with compactified extra dimensions.

But what you get from AdS/CFT are lowdimensional field theories in flat space being
equivalent to an AdS space times a compact space, containing strings and branes. The radial AdS dimension encodes the RG flow, and the compact space (and the objects with extension in it) is "made from" the space of ground states of the field theory. From this perspective, string theory is the universal theory of emergent RG geometry in quantum field theory. At the moment, it only works properly for an emergent AdS space, but if the dS/CFT correspondence can be understood, then this will be true for spaces of positive curvature as well. (In dS/CFT the boundary is purely spacelike and lies in the infinite past and future, rather than being timelike as in AdS/CFT, so it's as if the timelike direction in the Lorentzian gravitational space is emerging from Euclidean field theory on a sphere in the infinite past.)
So not only are people still doing flatspace string phenomenology, complete with branes and extra dimensions, but branes and extra dimensions have proved to be implicit in standard quantum field theory, where they emerge from the existence of a continuous degeneracy of ground states. That multidimensional moduli space of ground states is where the extra dimensions come from, in this case! Branes are domain walls separating regions in different ground states, strings are lines of flux connecting these domain walls. Furthermore, in gauge theories with a small number of colors, it looks like the extra dimensions will be a noncommutative geometry, it's only in the "large N" limit of many colors that you get ordinary space. (Consider that the noncommutative standard model of Connes et al is a theory of gravity on an "almost commutative" space  product of a Riemannian space and a finite noncommutative geometry  with the gauge bosons coming from gravity on the noncommutative part of the product geometry. This seems to be consistent with the picture coming from string theory.)