Abstract
We study the holographic dual of a (2+1)-dimensional s-wave superfluid that breaks an abelian U(1) x U(1) global symmetry group to the diagonal U(1)_V. The model is inspired by Sen's tachyonic action, and the operator that condenses transforms in the bifundamental representation of the symmetry group. We focus on two configurations: the first one describes a marginal operator, and the phase diagram at finite temperature contains a first or a second order phase transition, depending on the parameters that determine the theory. In the second model the operator is relevant and the finite temperature transitions are always second order. In the latter case the conductivity for the current associated to the broken symmetry shows quasiparticle excitations at low temperatures, with mass given by the width of the superconducting gap. The suppression of spectral weight at low frequencies is also observed in the conductivity associated to the conserved symmetry, for which the DC value decreases as the temperature is reduced.
Highlights
Black hole geometry.1 Effective brane-antibrane actions derived from string theory [16, 17] were first used in [18] to realize chiral symmetry breaking through tachyon condensation in a stack of overlapping branes and antibranes
We focus on two configurations: the first one describes a marginal operator, and the phase diagram at finite temperature contains a first or a second order phase transition, depending on the parameters that determine the theory
The main novelty of our model comes from the use of the tachyonic action describing a spacetime filling D3–D3 in an asymptotically AdS4 BH geometry
Summary
We will be interested in static solutions with rotational and translational invariance, . It is possible to recover the original holographic superconductor setup of [6] in a limit in which the DBI term in the action is linearized. Tb → 0, the equations of motion for the metric decouple from the equations of motion for the U(1) gauge field and the tachyon In this limit our system can be interpreted as a spacetime filling D3–D3 pair in the Schwarzschild-AdS4 spacetime, with the action describing the dynamics of the branes given by the DBI part of (2.7) alone. In unbalanced superconductors two different fermionic species with unbalanced populations contribute to the formation of superconducting states This imbalance, or chemical potential mismatch, can be described holographically by means of a second U(1) under which the order parameter is neutral [25] (see [24]). We do not pursue this direction in this paper, but leave it instead for future works
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