Andrei Starinets

Abstract:

We use gauge-gravity duality to study the temperature dependence of the zero sound mode and the fundamental matter diffusion mode in the strongly coupled N=4 SU(N c) supersymmetric Yang-Mills theory with N f N=2 hypermultiplets in the N c≫ 1, N c ≫ N f limit, which is holographically realized via the D3/D7 brane system. In the high density limit μ≫T, three regimes can be identified in the behavior of these modes, analogous to the collisionless quantum, collisionless thermal, and hydrodynamic regimes of a Landau Fermi liquid. The transitions between the three regimes are characterized by the parameters T/μ and (T/μ) 2, respectively, and in each of these regimes the modes have a distinctively different temperature and momentum dependence. The collisionless-hydrodynamic transition occurs when the zero sound poles of the density-density correlator in the complex frequency plane collide on the imaginary axis to produce a hydrodynamic diffusion pole. We observe that the properties characteristic of a Landau Fermi-liquid zero sound mode are present in the D3/D7 system despite the atypical T 6/μ 3 temperature scaling of the specific heat and an apparent lack of a directly identifiable Fermi surface. © 2012 American Physical Society.

Abstract:

Quasinormal modes are eigenmodes of dissipative systems. Perturbations of classical gravitational backgrounds involving black holes or branes naturally lead to quasinormal modes. The analysis and classification of the quasinormal spectra require solving non-Hermitian eigenvalue problems for the associated linear differential equations. Within the recently developed gauge-gravity duality, these modes serve as an important tool for determining the near-equilibrium properties of strongly coupled quantum field theories, in particular their transport coefficients, such as viscosity, conductivity and diffusion constants. In astrophysics, the detection of quasinormal modes in gravitational wave experiments would allow precise measurements of the mass and spin of black holes as well as new tests of general relativity. This review is meant as an introduction to the subject, with a focus on the recent developments in the field. © 2009 IOP Publishing Ltd.