Holographic non-Fermi-liquid fixed points

Abstract

Techniques arising from string theory can be used to study assemblies of strongly interacting fermions. Via this 'holographic duality', various strongly coupled many-body systems are solved using an auxiliary theory of gravity. Simple holographic realizations of finite density exhibit single-particle spectral functions with sharp Fermi surfaces, of a form distinct from those of the Landau theory. The self-energy is given by a correlation function in an infrared (IR) fixed-point theory that is represented by a two-dimensional anti de Sitter space (AdS 2 ) region in the dual gravitational description. Here, we describe in detail the gravity calculation of this IR correlation function.

Non-relativistic holography from Hořava gravity

“…In Section 5.4 a correlation function was calculated for a probe scalar on the background of AdS 2 × R 2 . The results show distinct non-relativistic characteristics, as compared to the relativistic calculations of [31,30] on this same background. Section 5.2 explores the class of solutions to Hořava gravity that asymptote to Lifshitz spacetimes.…”

“…While there are similarities between this correlation function and those calculated in [31,30], there are fundamental differences that reflect the non-relativistic nature of the current duality. From above, ν is strictly real and positive, while for relativistic charged scalars ν can become imaginary as the gauge coupling increases.…”

“…The near boundary behavior of the solution is of the form 37) where ∆ ± = 1 ± ν and determines the scaling dimension of the dual field theory operator to be ∆ + . Following [31,30], the retarded correlation function of the dual operator is given by the ratio of its expectation value, coming from the normalizable term r ∆ + , to its source value, coming from the non-normalizable term r ∆ − :…”

Charge transport by holographic Fermi surfaces

“…While it is fascinating that this set of results is self-consistent, we do stress that the marginal k F ¼ 1 2 point is not special from our gravity treatment, and more work needs to be done to understand if there is a way to single it out in holography. 17 …”

“…Recently, techniques from the AdS/CFT correspondence [11] have been used to find a class of non-Fermi liquids [12][13][14][15][16][17] (for a review see [18]). The low energy behavior of these non-Fermi liquids was shown to be governed by a nontrivial infrared (IR) fixed point which exhibits nonanalytic scaling behavior only in the time direction.…”