Monday, October 3, 2016

A critical review of holographic claims about condensed matter

There is a very helpful review article
Demystifying the Holographic Mystique by Dmitri Khveshchenko

In order to motivate a proper full reading I just give a few choice quotes.
Thus far, however, a flurry of the traditionally detailed (hence, rarely concise) publications on the topic have generated not only a good deal of enthusiasm but some reservations as well. Indeed, the proposed ’ad hoc’ generalizations of the original string-theoretical construction involve some of its most radical alterations, whereby most of its stringent constraints would have been aban- doned in the hope of still capturing some key aspects of the underlying correspondence. This is because the target (condensed matter) systems generically tend to be neither conformally, nor Lorentz (or even translationally and/or rotationally) invariant and lack any supersymmetric (or even an ordinary) gauge symmetry with some (let alone, large) rank-N non-abelian group. 
Moreover, while sporting a truly impressive level of technical profess, the exploratory ’bottom-up’ holographic studies have not yet helped to resolve such crucially important issues as: 
• Are the conditions of a large N, (super)gauge sym- metry, Lorentz/translational/rotational invariance of the boundary (quantum) theory indeed necessary for establishing a holographic correspondence with some weakly coupled (classical) gravity in the bulk? 
• Are all the strongly correlated systems (or only a precious few) supposed to have gravity duals? 
• What are the gravity duals of the already documented NFLs? 
• Given all the differences between the typical condensed matter and string theory problems, what (other than the lack of a better alternative) justifies the adaptation ’ad verbatim’ of the original (string-theoretical) holographic ’dictionary’? 
and, most importantly: 
• If the broadly defined holographic conjecture is indeed valid, then why is it so? 
Considering that by now the field of CMT holography has grown almost a decade old, it would seem that answering such outstanding questions should have been considered more important than continuing to apply the formal holographic recipes to an ever increasing number of model geometries and then seeking some resemblance to the real world systems without a good understanding as to why it would have to be there in the first place. In contrast, the overly pragmatic ’shut up and calculate’ approach prioritizes computational tractability over phys- ical relevance, thus making it more about the method (which readily provides a plethora of answers but may struggle to specify the pertinent questions) itself, rather than the underlying physics.

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