Silviu S. Pufu

The Gravity dual of a p-wave superconductor

We construct black hole solutions to the Yang-Mills equations in an AdS4-Schwarzschild background which exhibit superconductivity. What makes these backgrounds p-wave superconductors is that the order parameter is a vector, and the conductivities are strongly anisotropic in a manner that is suggestive of a gap with nodes. The low-lying excitations of the normal state have a relaxation time which grows rapidly as the temperature decreases, consistent with the absence of impurity scattering. A numerical exploration of quasinormal modes close to the transition temperature suggests that p-wave backgrounds are stable against perturbations analogous to turning on a p+ip gap, whereas p+ip-wave configurations are unstable against turning into pure p-wave backgrounds.

Superconductors from Superstrings

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=lambdalambda+W condenses. Here lambda is 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.

Multimatrix models and tri-Sasaki Einstein spaces

Localization methods reduce the path integrals in N{>=}2 supersymmetric Chern-Simons gauge theories on S{sup 3} to multimatrix integrals. A recent evaluation of such a two-matrix integral for the N=6 superconformal U(N)xU(N) Aharony-Bergman-Jafferis-Maldacena theory produced detailed agreement with the AdS/CFT correspondence, explaining, in particular, the N{sup 3/2} scaling of the free energy. We study a class of p-matrix integrals describing N=3 superconformal U(N){sup p} Chern-Simons gauge theories. We present a simple method that allows us to evaluate the eigenvalue densities and the free energies in the large N limit keeping the Chern-Simons levels k{sub i} fixed. The dual M-theory backgrounds are AdS{sub 4}xY, where Y are seven-dimensional tri-Sasaki Einstein spaces specified by the k{sub i}. The gravitational free energy scales inversely with the square root of the volume of Y. We find a general formula for the p-matrix free energies that agrees with the available results for volumes of the tri-Sasaki Einstein spaces Y, thus providing a thorough test of the corresponding AdS{sub 4}/CFT{sub 3} dualities. This formula is consistent with the Seiberg duality conjectured for Chern-Simons gauge theories.

F-Theorem without Supersymmetry

The conjectured F-theorem for three-dimensional field theories states that the finite part of the free energy on S3 decreases along RG trajectories and is stationary at the fixed points. In previous work various successful tests of this proposal were carried out for theories with

Entropy production in collisions of gravitational shock waves and of heavy ions

\mathcal{N} = 2

Thermodynamics and bulk viscosity of approximate black hole duals to finite temperature quantum chromodynamics

supersymmetry. In this paper we perform more general tests that do not rely on supersymmetry. We study perturbatively the RG flows produced by weakly relevant operators and show that the free energy decreases monotonically. We also consider large N field theories perturbed by relevant double trace operators, free massive field theories, and some non-Abelian gauge theories. In all cases the free energy in the IR is smaller than in the UV, consistent with the F-theorem. We discuss other odd-dimensional Euclidean theories on Sd and provide evidence that (−1)(d−1)/2 log|Z| decreases along RG flow; in the particular case d = 1 this is the well-known g-theorem.

Bulk viscosity of strongly coupled plasmas with holographic duals

We calculate the area of a marginally trapped surface formed by a head-on collision of gravitational shock waves in AdS{sub D}. We use this to obtain a lower bound on the entropy produced after the collision. A comparison to entropy production in heavy-ion collisions is included. We also discuss an O(D-2) remnant of conformal symmetry, which is present in a class of gravitational shockwave collisions in AdS{sub D} and which might be approximately realized (with D=5) in central heavy-ion collisions.

Gluon energy loss in the gauge-string duality

We consider classes of translationally invariant black hole solutions whose equations of state closely resemble that of QCD at zero chemical potential. We use these backgrounds to compute the ratio zeta/s of bulk viscosity to entropy density. For a class of black holes that exhibits a first-order transition, we observe a sharp rise in zeta/s near Tc. For constructions that exhibit a smooth crossover, like QCD does, the rise in zeta/s is more modest. We conjecture that divergences in zeta/s for black hole horizons are related to extrema of the entropy density as a function of temperature.

Expanding plasmas and quasinormal modes of anti-de Sitter black holes

We explain a method for computing the bulk viscosity of strongly coupled thermal plasmas dual to supergravity backgrounds supported by one scalar field. Whereas earlier investigations required the computation of the leading dissipative term in the dispersion relation for sound waves, our method requires only the leading frequency dependence of an appropriate Greens function in the low-frequency limit. With a scalar potential chosen to mimic the equation of state of QCD, we observe a slight violation of the lower bound on the ratio of the bulk and shear viscosities conjectured in [1].

Quantum critical superconductors in string theory and M-theory

We estimate the stopping length of an energetic gluon in a thermal plasma of strongly coupled = 4 super-Yang-Mills theory by representing the gluon as a doubled string rising up out of the horizon.