An Introduction to Gauge Gravity Duality and Its Application in Condensed Matter

Abstract

The past few years have witnessed a remarkable crossover of string theoretical ideas from the abstract world of geometrical forms to the concrete experimental realm of condensed matter physics. The basis for this --- variously known as holography, the AdS/CFT correspondence or gauge-gravity duality --comes from notions right at the cutting edge of string theory. Nevertheless, the insights afforded can often be expressed in ways very familiar to condensed matter physicists, such as relationships between response functions and new sum rules. The aim of this short, introductory review is to survey the ideas underpinning this crossover, in a way that -- as far as possible -- strips them of sophisticated mathematical formalism, whilst at the same time retaining their fundamental essence. I will sketch the areas in which progress has been made to date and highlight where the challenges and open questions lie. Finally, I will attempt to give a perspective upon these ideas. What contribution can we realistically expect from this approach and how might it be accommodated into the canon of condensed matter theory? Inevitably, any attempt to do this in such a rapidly evolving field will be superseded by events. Nevertheless, I hope that this will provide a useful way to think about gauge-gravity duality and the uncharted directions in which it might take us.

Unedited version of article published in Contemporary Physics. Intended for advanced final-year undergraduates

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• A class of quantum many-body states that can be efficiently simulated
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• Fractionalized Fermi liquids
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• Holographic superconductivity in M-Theory
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Cited by in corpus (11)

• A Holographic Model of the Kondo Effect
• Holographic Competition of Phases and Superconductivity
• Holographic correspondence in topological superconductors
• P-wave holographic superconductor/insulator phase transitions affected by dark matter sector
• Nonlinear Transport in a Two Dimensional Holographic Superconductor
• Nonlinear Conductivity of a Holographic Superconductor Under Constant Electric Field
• Holographic vortices in the presence of dark matter sector
• Hyperscaling violating geometry with magnetic field and DC conductivity
• Holographic superconductivity in the presence of dark matter: basic issues
• The Emergence of Superconducting Systems in Anti-de Sitter Space
• Metallic and antiferromagnetic fixed points from gravity