Giuseppe Policastro

From AdS/CFT correspondence to hydrodynamics

We compute the correlation functions of R-charge currents and components of the stress-energy tensor in the strongly coupled large-N finite-temperature = 4 supersymmetric Yang-Mills theory, following a recently formulated minkowskian AdS/CFT prescription. We observe that in the long-distance, low-frequency limit, such correlators have the form dictated by hydrodynamics. We deduce from the calculations the R-charge diffusion constant and the shear viscosity. The value for the latter is in agreement with an earlier calculation based on the Kubo formula and absorption by black branes.We compute the correlation functions of R-charge currents and components of the stress-energy tensor in the strongly coupled large-N finite-temperature N=4 supersymmetric Yang-Mills theory, following a recently formulated Minkowskian AdS/CFT prescription. We observe that in the long-distance, low-frequency limit, such correlators have the form dictated by hydrodynamics. We deduce from the calculations the R-charge diffusion constant and the shear viscosity. The value for the latter is in agreement with an earlier calculation based on the Kubo formula and absorption by black branes.

From AdS/CFT correspondence to hydrodynamics. II. Sound waves

As a non-trivial check of the non-supersymmetric gauge/gravity duality, we use a near-extremal black brane background to compute the retarded Green’s functions of the stress-energy tensor in N = 4 super-Yang-Mills (SYM) theory at finite temperature. For the long-distance, low-frequency modes of the diagonal components of the stress-energy tensor, hydrodynamics predicts the existence of a pole in the correlators corresponding to propagation of sound waves in the N = 4 SYM plasma. The retarded Green’s functions obtained from gravity do indeed exhibit this pole, with the correct values for the sound speed and the rate of attenuation.As a non-trivial check of the non-supersymmetric gauge/gravity duality, we use a near-extremal black brane background to compute the retarded Greens functions of the stress-energy tensor in = 4 super-Yang-Mills (SYM) theory at finite temperature. For the long-distance, low-frequency modes of the diagonal components of the stress-energy tensor, hydrodynamics predicts the existence of a pole in the correlators corresponding to propagation of sound waves in the = 4 SYM plasma. The retarded Greens functions obtained from gravity do indeed exhibit this pole, with the correct values for the sound speed and the rate of attenuation.

Holographic optics and negative refractive index

In recent years a very exciting and intense activity has been devoted to the understanding and construction of materials that enjoy exotic optical properties, such as a negative refractive index. Motivated by these experimental and theoretical developments, we use the string-inspired idea of holography to study the electromagnetic response of a certain class of media: strongly coupled relativistic systems that admit a dual gravitational description. Our results indicate that this type of media generally have a negative refractive index. Moreover we observe that a negative refractive index could be a common feature of relativistic hydrodynamic systems at low frequencies.

Flavor corrections to the entanglement entropy

A bstractWe consider the holographic entanglement entropy in

Conformal blocks and negativity at large central charge

\mathcal{N}

Supersymmetric hydrodynamics from the AdS/CFT correspondence

= 4 SYM coupled to massive flavor degrees of freedom. The flavors are introduced by putting D7 branes in AdS5. The resulting geometry including the backreaction of the branes is known in a perturbation expansion in the ratio Nf/Nc. We consider the expansion to first order, and compute the entanglement entropy of a region of the boundary. We consider two different cases for the geometry of the region: a slab and a ball. We find analytic solutions for the minimal surfaces in the bulk whose area gives the entropy, and analyze the structure of the UV divergence and the dependence on the masses. Our results confirm the general structure that was predicted by free field theory calculations, but with coefficients that depend on the coupling.

Dressing the electron star in a holographic superconductor

A bstractWe consider entanglement negativity for two disjoint intervals in 1+1 dimensional CFT in the limit of large central charge. As the two intervals get close, the leading behavior of negativity is given by the logarithm of the conformal block where a set of approximately null descendants appears in the intermediate channel. We compute this quantity numerically and compare with existing analytic methods which provide perturbative expansion in powers of the cross-ratio.

Diffusion constant of supercharge density in N = 4 SYM at finite chemical potential

We compute holographically the dispersion relation for a hydrodynamic mode of fluctuation (the phonino) of the density of supersymmetry current in = 4 SYM at strong coupling. The mode appears as a pole at low frequency and momentum in the correlator of supercurrents. It has a wave-like propagation, and we find its speed and coefficient of attenuation.

A note on the quartic effective action of the type IIB superstring

A bstractWe construct new asymptotically AdS4 solutions dual to 2+1 CFTs at finite density and zero temperature by combining the ingredients of the electron star and the holographic superconductor. The solutions, which we call compact electron stars, contain both a fermionic fluid and charged scalar hair in the bulk. We show that the new solutions are thermodynamically favoured in the region of parameter space where they exist. Along the boundary of this region, we find evidence for a continuous phase transition between the holographic superconductor and the compact star solution.

Late time behavior of non-conformal plasmas

A bstractWe compute holographically the diffusion constant of supercharges in N = 4 SYM at finite chemical potential for the R-charge, by solving the equations of motion for the transverse mode of the gravitino in the STU black hole in 5 dimensions. We consider the case of one charge and three charges, and we present analytical solutions for small values of the charges and numerical solutions for arbitrary values. We compare our results with other known results in 4 dimensions.