Abstract
We argue that there exist simple effective field theories describing the long-distance dynamics of holographic liquids. The degrees of freedom responsible for the transport of charge and energy–momentum are Goldstone modes. These modes are coupled to a strongly coupled infrared (IR) sector through emergent gauge and gravitational fields. The IR degrees of freedom are described holographically by the near-horizon part of the metric, whereas the Goldstone bosons are described by a field-theoretical Lagrangian. In the cases where the holographic dual involves a black hole, this picture allows for a direct connection between the holographic prescription where currents live on the boundary and the membrane paradigm where currents live on the horizon. The zero-temperature sound mode in the D3–D7 system is also re-analyzed and re-interpreted within this formalism.
Highlights
There is considerable interest in using holographic methods [1,2,3] to study strongly coupled quantum liquids
We suggest that the long-distance description of holographic liquids involve a set of Goldstone bosons in addition to the degrees of freedom living in the near horizon region
We show that the diffusion mode can be interpreted as a Goldstone boson, which is coupled, through an emergent gauge field, to a stretched horizon with a finite electrical conductivity
Summary
There is considerable interest in using holographic methods [1,2,3] to study strongly coupled quantum liquids. The AdS2 infrared asymptotics of the Reissner-Nordstrom metric, which is supposed to describe a finite-density, zero-temperature system, should correspond to a (0+1)-dimensional conformal field theory, the nature of such a theory is not very clear It has been seen explicitly in many calculations that the near-horizon geometry influences the singular behavior of the inverse propagators [10]. We suggest that the long-distance description of holographic liquids involve a set of Goldstone bosons in addition to the degrees of freedom living in the near horizon region. We can visualize the process of finding the low-energy effective theory as a Wilsonian renormalization group procedure In this language, the Goldstone boson appears as the only mode living outside the near-horizon part of the metric that survives this procedure.
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