# Publications by Andrei Starinets

## Adding new branches to the “Christmas tree” of the quasinormal spectrum of black branes

Journal of High Energy Physics Springer Nature **2019** (2019) 80

## Convergence of the Gradient Expansion in Hydrodynamics

Physical Review Letters American Physical Society (APS) **122** (2019) 251601

## Transport peak in thermal spectral function of ${\cal N}=4$ supersymmetric Yang-Mills plasma at intermediate coupling

Physical Review Letters American Physical Society (2018)

We study the structure of thermal spectral function of the stress-energy tensor in ${\cal N}=4$ supersymmetric Yang-Mills theory at intermediate 't Hooft coupling and infinite number of colors. In gauge-string duality, this analysis reduces to the study of classical bulk supergravity with higher-derivative corrections, which correspond to (inverse) coupling corrections on the gauge theory side. We extrapolate the analysis of perturbative leading-order corrections to intermediate coupling by non-perturbatively solving the equations of motion of metric fluctuations dual to the stress-energy tensor at zero spatial momentum. We observe the emergence of a separation of scales in the analytic structure of the thermal correlator associated with two types of characteristic relaxation modes. As a consequence of this separation, the associated spectral function exhibits a narrow structure in the small frequency region which controls the dynamics of transport in the theory and may be described as a transport peak typically found in perturbative, weakly interacting thermal field theories. We compare our results with generic expectations drawn from perturbation theory, where such a structure emerges as a consequence of the existence of quasiparticles.

## Second-order transport, quasinormal modes and zero-viscosity limit in the Gauss-Bonnet holographic fluid

Journal of High Energy Physics **2017** (2017)

© 2017, The Author(s). Gauss-Bonnet holographic fluid is a useful theoretical laboratory to study the effects of curvature-squared terms in the dual gravity action on transport coefficients, quasinormal spectra and the analytic structure of thermal correlators at strong coupling. To understand the behavior and possible pathologies of the Gauss-Bonnet fluid in 3 + 1 dimensions, we compute (analytically and non-perturbatively in the Gauss-Bonnet coupling) its second-order transport coefficients, the retarded two- and three-point correlation functions of the energy-momentum tensor in the hydrodynamic regime as well as the relevant quasinormal spectrum. The Haack-Yarom universal relation among the second-order transport coefficients is violated at second order in the Gauss-Bonnet coupling. In the zero-viscosity limit, the holographic fluid still produces entropy, while the momentum diffusion and the sound attenuation are suppressed at all orders in the hydrodynamic expansion. By adding higher-derivative electromagnetic field terms to the action, we also compute corrections to charge diffusion and identify the non-perturbative parameter regime in which the charge diffusion constant vanishes.

## From strong to weak coupling in holographic models of thermalization

Journal of High Energy Physics **2016** (2016)

© 2016, The Author(s). Abstract: We investigate the analytic structure of thermal energy-momentum tensor correlators at large but finite coupling in quantum field theories with gravity duals. We compute corrections to the quasinormal spectra of black branes due to the presence of higher derivative R2 and R4 terms in the action, focusing on the dual to N= 4 SYM theory and Gauss-Bonnet gravity. We observe the appearance of new poles in the complex frequency plane at finite coupling. The new poles interfere with hydrodynamic poles of the correlators leading to the breakdown of hydrodynamic description at a coupling-dependent critical value of the wave-vector. The dependence of the critical wave vector on the coupling implies that the range of validity of the hydrodynamic description increases monotonically with the coupling. The behavior of the quasinormal spectrum at large but finite coupling may be contrasted with the known properties of the hierarchy of relaxation times determined by the spectrum of a linearized kinetic operator at weak coupling. We find that the ratio of a transport coefficient such as viscosity to the relaxation time determined by the fundamental non-hydrodynamic quasinormal frequency changes rapidly in the vicinity of infinite coupling but flattens out for weaker coupling, suggesting an extrapolation from strong coupling to the kinetic theory result. We note that the behavior of the quasinormal spectrum is qualitatively different depending on whether the ratio of shear viscosity to entropy density is greater or less than the universal, infinite coupling value of ℏ/4πkB. In the former case, the density of poles increases, indicating a formation of branch cuts in the weak coupling limit, and the spectral function shows the appearance of narrow peaks. We also discuss the relation of the viscosity-entropy ratio to conjectured bounds on relaxation time in quantum systems.

## Zero-viscosity limit in a holographic Gauss-Bonnet liquid

THEORETICAL AND MATHEMATICAL PHYSICS **182** (2015) 61-73

## On the universal identity in second order hydrodynamics

JOURNAL OF HIGH ENERGY PHYSICS (2015) ARTN 007

## Holographic zero sound at finite temperature

PHYSICAL REVIEW D **85** (2012) ARTN 026004

## Holographic zero sound at finite temperature

Physical Review D - Particles, Fields, Gravitation and Cosmology **85** (2012)

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.

## Quasinormal modes of black holes and black branes

Classical and Quantum Gravity **26** (2009)

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.

## Holographic quantum liquid

Physical Review Letters **102** (2009)

Quantum liquids are characterized by the distinctive properties such as the low-temperature behavior of heat capacity and the spectrum of low-energy quasiparticle excitations. In particular, at low temperature, Fermi liquids exhibit the zero sound, predicted by Landau in 1957 and subsequently observed in liquid He-3. In this Letter, we ask whether such characteristic behavior is present in theories with a holographically dual description. We consider a class of gauge theories with fundamental matter fields whose holographic dual in the appropriate limit is given in terms of the Dirac-Born-Infeld action in anti-de Sitter space. We find that these systems also exhibit a sound mode at zero temperature despite having a non-Fermi-liquid behavior of the specific heat. These properties suggest that holography identifies a new type of quantum liquid which potentially could be experimentally realized in strongly correlated systems. © 2009 The American Physical Society.

## Quasinormal spectrum and the black hole membrane paradigm

Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics **670** (2009) 442-445

The membrane paradigm approach to black hole physics introduces the notion of a stretched horizon as a fictitious time-like surface endowed with physical characteristics such as entropy, viscosity and electrical conductivity. We show that certain properties of the stretched horizons are encoded in the quasinormal spectrum of black holes. We compute analytically the lowest quasinormal frequency of a vector-type perturbation for a generic black hole with a translationally invariant horizon (black brane) in terms of the background metric components. The resulting dispersion relation is identical to the one obtained in the membrane paradigm treatment of the diffusion on stretched horizons. Combined with the Buchel-Liu universality theorem for the membrane's diffusion coefficient, our result means that in the long wavelength limit the black brane spectrum of gravitational perturbations exhibits a universal, purely imaginary quasinormal frequency. In the context of gauge-gravity duality, this provides yet another (third) proof of the universality of shear viscosity to entropy density ratio in theories with gravity duals. © 2008 Elsevier B.V. All rights reserved.

## Relativistic viscous hydrodynamics, conformal invariance, and holography

Journal of High Energy Physics **2008** (2008)

We consider second-order viscous hydrodynamics in conformal field theories at finite temperature. We show that conformal invariance imposes powerful constraints on the form of the second-order corrections. By matching to the AdS/CFT calculations of correlators, and to recent results for Bjorken flow obtained by Heller and Janik, we find three (out of five) second-order transport coefficients in the strongly coupled = 4 supersymmetric Yang-Mills theory. We also discuss how these new coefficents can arise within the kinetic theory of weakly coupled conformal plasmas. We point out that the Müller-Israel- Stewart theory, often used in numerical simulations, does not contain all allowed second-order terms and, frequently, terms required by conformal invariance.

## Viscosity, black holes, and quantum field theory

Annual Review of Nuclear and Particle Science **57** (2007) 95-118

We review recent progress in applying the AdS/CFT correspondence to finite-temperature field theory. In particular, we show how the hydrodynamic behavior of field theory is reflected in the low-momentum limit of correlation functions computed through a real-time AdS/CFT prescription, which we formulate. We also show how the hydrodynamic modes in field theory correspond to the low-lying quasi-normal modes of the AdS black p-brane metric. We provide proof of the universality of the viscosity/entropy ratio within a class of theories with gravity duals and formulate a viscosity bound conjecture. Possible implications for real systems are mentioned. Copyright © 2007 by Annual Reviews. All rights reserved.

## Holographic spectral functions and diffusion constants for fundamental matter

Journal of High Energy Physics **2007** (2007)

The holographic dual of large-N c super-Yang-Mills coupled to a small number of flavours of fundamental matter, N f << N c, is described by N f probe D7-branes in the gravitational background of N c black D3-branes. This system undergoes a first order phase transition characterised by the 'melting' of the mesons. We study the high temperature phase in which the D7-branes extend through the black hole horizon. In this phase, we compute the spectral function for vector, scalar and pseudoscalar modes on the D7-brane probe. We also compute the diffusion constant for the flavour currents. © SISSA 2007.

## Sound waves in strongly coupled non-conformal gauge theory plasma

Nuclear Physics B **733** (2006) 160-187

Using gauge theory/gravity duality we study sound wave propagation in strongly coupled non-conformal gauge theory plasma. We compute the speed of sound and the bulk viscosity of N = 2* supersymmetric SU(Nc) Yang-Mills plasma at a temperature much larger than the mass scale of the theory in the limit of large Nc and large 't Hooft coupling. The speed of sound is computed both from the equation of state and the hydrodynamic pole in the stress-energy tensor two-point correlation function. Both computations lead to the same result. Bulk viscosity is determined by computing the attenuation constant of the sound wave mode. © 2005 Elsevier B.V. All rights reserved.

## Transport coefficients of strongly coupled gauge theories: Insights from string theory

European Physical Journal A **29** (2006) 77-81

The transport properties of certain strongly coupled thermal gauge theories can be determined from their effective description in terms of gravity or superstring theory duals. Here we provide a short summary of the results for the shear and bulk viscosity, charge diffusion constant, and the speed of sound in supersymmetric strongly interacting plasmas. We also outline a general algorithm for computing transport coefficients in any gravity dual. The algorithm relates the transport coefficients to the coefficients in the quasinormal spectrum of five-dimensional black holes in asymptotically anti de Sitter space.

## Thermal spectral functions of strongly coupled N = 4 supersymmetric Yang-Mills theory.

Phys Rev Lett **96** (2006) 131601-

We use the gauge-gravity duality conjecture to compute spectral functions of the stress-energy tensor in finite-temperature N = 4 supersymmetric Yang-Mills theory in the limit of large N(c) and large 't Hooft coupling. The spectral functions exhibit peaks characteristic of hydrodynamic modes at small frequency, and oscillations at intermediate frequency. The nonperturbative spectral functions differ qualitatively from those obtained in perturbation theory. The results may prove useful for lattice studies of transport processes in thermal gauge theories.

## Hydrodynamics of R-charged black holes

Journal of High Energy Physics (2006) 1291-1309

We consider hydrodynamics of = 4 supersymmetric SU(Nc) Yang-Mills plasma at a nonzero density of R-charge. In the regime of large Nc and large 't Hooft coupling the gravity dual description involves an asymptotically Anti- de Sitter five-dimensional charged black hole solution of Behrnd, Cvetic and Sabra. We compute the shear viscosity as a function of chemical potentials conjugated to the three U(1)SO(6) R charges. The ratio of the shear viscosity to entropy density is independent of the chemical potentials and is equal to 1/4π. For a single charge black hole we also compute the thermal conductivity, and investigate the critical behavior of the transport coefficients near the boundary of thermodynamic stability. © SISSA 2006.