Condensed Matter and AdS/CFT

Abstract

I review two classes of strong coupling problems in condensed matter physics, and describe insights gained by application of the AdS/CFT correspondence. The first class concerns non-zero temperature dynamics and transport in the vicinity of quantum critical points described by relativistic field theories. I describe how relativistic structures arise in models of physical interest, present results for their quantum critical crossover functions and magneto-thermoelectric hydrodynamics. The second class concerns symmetry breaking transitions of twodimensional systems in the presence of gapless electronic excitations at isolated points or along lines (i.e. Fermi surfaces) in the Brillouin zone. I describe the scaling structure of a recent theory of the Ising-nematic transition in metals, and discuss its possible connection to theories of Fermi surfaces obtained from simple AdS duals.

What do non-relativistic CFTs tell us about Lifshitz spacetimes?

“…As a result, we will end up setting A = 0 and investigating the consequences of doing so. 4 Turning now to the horizon, we see that both terms in (3.14) fall off as ζ → ∞. Hence the horizon behavior is given by 5…”

“…Particularly in these cases it appears more difficult to redefine the Hamiltonian in the usual way [55][56][57]. 4 Note that this is in contrast with the computation of AdS/CFT correlators, where B is interpreted as the response to turning on a source A. 5 For simplicity, we have assumed 1 < k < 2.…”

“…These non-relativistic forms of AdS/CFT, often collectively referred to as AdS/CMT due to their relevance for condensed matter systems, have provided a new tool for examining strongly coupled non-relativistic systems (see, e.g. [1][2][3][4] and references therein).…”

Lifshitz black holes in IIA supergravity

“…The typical set-up uses the concept of gauge/gravity duality [1] in which a classical gravitational system with negative spacetime curvature has, on its boundary, equivalent degrees of freedom to a strongly coupled gauge theory. Temperature is gravitationally introduced into these systems by adding a black hole in the bulk spacetime, and different holographic dual theories can be constructed by having additional bulk fields (see [2,3] for reviews of this approach).…”

Rotating black holes in 4d gauged supergravity

“…Alternatively, these gravitational systems provide non-trivial asymptotically AdS backgrounds with holographic duals that exhibit a rich structure and a wide range of applications in field theory and condensed matter systems, see e.g. [14][15][16][17][18][19].…”