Holography Light: Justification and Future Theory

Table of Links

• Prologue
• Diagrammatic(s) Rules
• Straight-forward Eikonal
• Legacy Bosonization
• Wonton Holography
• Holographic Propagators
• Strange Cuprates
• Stranger Things
• Epilogue

Epilogue

Importantly, even a perfect match between the holographic and some other (believed to be comparatively better established) results would not provide a firm justification for the holographic technique itself. Indeed, any results obtained under the assumption of a purely classical (non-dynamical) background metric - which assumption is overwhelmingly common to the practical applications of the holographic approach - would only pertain to its ’light’ version, as opposed to the full-fledged one. As to the possible desk-top simulations of such a ’holography light’ scenario, those have been proposed for several platforms, including flexible graphene flakes [55] and hyperbolic metamaterials [56].

Projecting into the future, it seems quite likely that the ultimate theory of correlated quantum matter will eventually assume a form akin to quantum hydrodynamics formulated in terms of the moments of quantum distribution function [57]. Such a collective-field description of the bulk (a.k.a. ’phase’) space with the d-dimensional momentum providing for the extra dimensions could be equally well called either bosonization, or holography. Regardless of the name, though, taking a full advantage of this formally exact approach might turn out to be difficult, especially in the physically relevant cases of N ∼ 1 and moderate coupling strengths.

Nevertheless, there still seems to be no good reason neither for this theory to conform to anything as specific and convenient as the EMD Lagrangian (22), nor for the corresponding holographic dictionary to be copy-pasted ’ad verbatim’ from string/HEP theory.

One would hope that exposing the existing controversy over this and related issues might be helpful to authors of the future original (of course) studies on the topic - as well as their knowledgeable and unbiased (of course) referees.

This note was compiled, in part, while staying at and being supported by the Aspen Center for Physics under the NSF Grant PHY-1607611.

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