“The violation of the holographic duality bound is based on DMFT calculations, which is a bit like string theory for strongly correlated fermions in the sense that it is somtimes sold as “the only game in town”. Nobody knows how accurate these methods really are.”

I disagree. My detailed response is here.

]]>Why does nobody say anything about the almost one year delay in the announcement of the Lucasian chair occupant? It is a rather curious situation for such a prestigious professorship.

Sam

]]>I’m certainly no expert on AdS/CFT, but as I understand it, the geometric setting for the theory is an asymptotically hyperbolic manifold: take a compact manifold-with-boundary \bar{M} and put a metric g on the interior (M) such that g blows up to second-order. Then for any defining function f of the boundary (f is zero precisely on the boundary and df is nonvanishing there), f^2g is a metric on the whole manifold-with-boundary. We can choose different functions f, and so restricting f^2g to the boundary, we induce a conformal class of metrics there (but not a well-defined Riemannian metric). Hence the *conformal* in the CFT. The interior metric can then be expanded in a well-defined way in powers of the defining function, where the coefficients are determined by the conformal geometry of the boundary, say N.

The problem is that the curvature of the interior metric is asymptotically -|df|^2, where this norm is taken in the metric f^2g. Thus, we can have negative-curvature metrics on the interior, or maybe asymptotically flat ones, but we can’t have positive-curvature ones.

This I *think* is the reason, but I don’t claim to know a lot about Lorentzian geometry, or (goodness knows) the AdS/CFT conjecture.

]]>I’ve also heard it claimed that one could think of the 5th dimension in terms of the renormalization group flow. Again, I’ve never seen a precise statement. ]]>

His observation in 1957, at the age of 26, that scattering amplitudes in non-relativistic quantum mechanics are controlled by poles in the complex angular momentum plane led in 1967 to the Veneziano amplitude and from there to almost everything discussed in this blog.

]]>Maybe someone else has a good answer. My problem is that I don’t really understand why AdS/CFT, so no idea about why no dS/CFT. Many of the general arguments about the ubiquity of holography seem to apply to either dS or AdS. ]]>