Superconductors from Superstrings

TL;DR

The authors embed holographic superconductivity in a broad class of strongly coupled 3+1D N=1 SCFTs by constructing a consistent five-dimensional truncation of type IIB supergravity with a U(1) R-symmetry gauge field and a complex scalar dual to a chiral primary O of Δ=3. Under a chemical potential for R-charge, the dual AdS black hole develops hair, signaling a second-order U(1) symmetry-breaking phase transition and enabling a microscopic string-theory description of the condensate O ∼ W + ∑ Tr λ^2. They analyze perturbative instabilities to map the Tc landscape via a Tp(Δ,R) threshold, arguing that the O with Δ=3 typically dominates in CY quivers, though some theories possess lower-dimension primaries that can alter the dynamics. They further propose O as a universal chiral primary operator in CY cone quivers, with explicit examples like S^5/ℤ7 where O is among the lowest-dimension primaries, thereby providing a concrete holographic mechanism for superfluid transitions in string theory contexts.

Abstract

We establish that in a large class of strongly coupled 3+1 dimensional N=1 quiver conformal field theories with gravity duals, adding a chemical potential for the R-charge leads to the existence of superfluid states in which a chiral primary operator of the schematic form O = λλ+ W condenses. Here λis a gluino and W is the superpotential. Our argument is based on the construction of a consistent truncation of type IIB supergravity that includes a U(1) gauge field and a complex scalar.

Figures (2)

• Figure 1: (Color online.) Upper right plot: $\lvert \langle {\cal O} \rangle \rvert^{1/3} / T_0$ vs. $T/T_0$, where $\langle {\cal O} \rangle$ is expressed as multiples of $L^3/ \kappa_5^2$. The critical temperature is $T_0 \approx 0.0607 \mu$. Near $T_0$, $\langle {\cal O} \rangle \sim \lvert T - T_0 \rvert^{1/2}$, indicating a mean field critical exponent. Lower left plot: $\Delta P / T^4$ vs. $T/T_0$, where $\Delta P$ is the difference in pressure between the broken and unbroken phases, calculated in the grand canonical ensemble. Near $T_0$, one has $\Delta P \sim (T-T_0)^2$, so the phase transition is second order.
• Figure 2: (Color online.) A contour plot of $T_p/\mu$ as a function of $\Delta$ and $R$. The numbers next to the contour lines represent $T_p/\mu$. We need only consider scalars above the unitarity bound, $\Delta \geq 1$Mack:1975je. The dark solid line is the BPS bound $\Delta = 3 R/2$Dobrev:1985qv. Scalars which are less stable than the operator $\mathcal{O}$ are restricted to the triangular, shaded region near the lower-left corner.