It is one of many quasi-journalistic discussions I have seen of results using the AdS/CFT (anti–de Sitter/conformal field theory) correspondence from quantum gravitation theory ostensibly to solve condensed-matter physics problems such as the “strange metal” in the cuprate (high Tc) superconducting metals.I think the following criticism is particularly important:
The strange-metal region of the cuprate phase diagram exhibits not only a linear dependence on temperature of the conductivity relaxation rate, which is generally taken by string theorists as the characteristic symptom identifying a strange metal and is the only feature they discuss.There are many other properties of the strange metal.
Anderson lists the "Drude tail" in the infra-red region of the frequency dependent conductivity, the temperature dependence of the Hall angle, and power-law dependence of the various spectra. Any decent theory must also explain all these other features.
Anderson then claims that this phenomenology is all described by his hidden Fermi liquid theory, culminating in a 2011 PRL he wrote with Phil Casey.
I disagree on this point. A PRL by Jure Kokalj and I showed this theory could not explain the doping and temperature dependence of the scattering rate deduced from angle-dependent magnetoresistance measurements in the overdoped region (i.e. dopings larger than that of the strange metal phase).
A PRB by Jure, Nigel Hussey, and I shows how a model self energy can describe the frequency, temperature, and doping dependence of the properties of metal at overdoping. However, this does not give a microscopic explanation or describe the strange metal.
Anderson also mentions a connection of his theory to the chiral anomaly [Jackiw-Rebbi] in field theory.
[I think this is the "parity anomaly" in Haldane's famous "Quantum Hall effect without Landau levels" paper].
I don't follow this connection at all.
Anderson concludes by suggesting that most condensed matter systems are not relativistic and conformal, particularly due to the presence of the lattice.
I did not find Hong Liu's response to Anderson's letter particularly convincing. To me it just highlights all of the assumptions [and wishful thinking?] implicit in the AdS/CFT approach.
What do you think?
It should also be pointed out that even if AdS/CFT is an appropriate effective field theory for the strange metal, the important question will remain: How does that effective theory emerge from the underlying microscopic Hamiltonian?