Nabil Iqbal

Real-time response in AdS/CFT with application to spinors

We discuss a simple derivation of the real-time AdS/CFT prescription as an analytic continuation of the corresponding problem in Euclidean signature. We then extend the formalism to spinor operators and apply it to the examples of real-time fermionic correlators in CFTs dual to pure AdS and the BTZ black hole.

Wilson Lines and Entanglement Entropy in Higher Spin Gravity

A bstractHolographic entanglement entropy provides a direct connection between classical geometry and quantum entanglement; however the usual prescription does not apply to theories of higher spin gravity, where standard notions of geometry are no longer gauge invariant. We present a proposal for the holographic computation of entanglement entropy in field theories dual to higher spin theories of gravity in AdS3. These theories have a Chern-Simons description, and our proposal involves a Wilson line in an infinite-dimensional representation of the bulk gauge group. In the case of spin−2 gravity such Wilson lines are the natural coupling of a heavy point particle to gravity and so are equivalent to the usual prescription of Ryu and Takayanagi. For higher spin gravity they provide a natural generalization of these ideas. We work out spin−3 gravity in detail, showing that our proposal recovers many expected results and computes thermal entropies of black holes with higher spin charge, finding agreement with previous expressions in the literature. We encounter some peculiarities in the case of non-unitary RG flow backgrounds and outline future generalizations.

Semi-local quantum liquids

A bstractGauge/gravity duality applied to strongly interacting systems at finite density predicts a universal intermediate energy phase to which we refer as a semi-local quantum liquid. Such a phase is characterized by a finite spatial correlation length, but an infinite correlation time and associated nontrivial scaling behavior in the time direction, as well as a nonzero entropy density. For a holographic system at a nonzero chemical potential, this unstable phase sets in at an energy scale of order of the chemical potential, and orders at lower energies into other phases; examples include superconductors, and antiferromagnetic-type states. In this paper we give examples in which it also orders into Fermi liquids of “heavy” fermions. While the precise nature of the lower energy state depends on the specific dynamics of the individual system, we argue that the semi-local quantum liquid emerges universally at intermediate energies through deconfinement (or equivalently fractionalization). We also discuss the possible relevance of such a semi-local quantum liquid to heavy electron systems and the strange metal phase of high temperature cuprate superconductors.

Strange Metal Transport Realized by Gauge/Gravity Duality

Black Holes as Tools When confronted with a difficult problem, physicists often resort to mapping it to a more tractable one. A good example of this strategy is provided by new developments linking string theory and condensed-matter physics to make theoretical connections between gravity and complex systems of interacting electrons. This theoretical convergence provides a description of Fermi liquids, which can be thought of as interacting systems of electrons whose excitations can be expressed in terms of non-interacting quasiparticles. Several interesting systems elude quasiparticle description, but Faulkner et al. (p. 1043, published online 5 August) have now developed a mathematical framework that describes the non-Fermi liquid represented by the strange metal phase of cuprate high-temperature superconductors. They calculate the electronic response and, for a particular value of a tunable parameter, recover the linear resistivity. Further development of this framework may allow elucidation of other exotic properties of the cuprates and similar complex systems. Black hole theory is used to develop a mathematical description of a class of metals with unusual electronic properties. Fermi liquid theory explains the thermodynamic and transport properties of most metals. The so-called non-Fermi liquids deviate from these expectations and include exotic systems such as the strange metal phase of cuprate superconductors and heavy fermion materials near a quantum phase transition. We used the anti–de-Sitter/conformal field theory correspondence to identify a class of non-Fermi liquids; their low-energy behavior is found to be governed by a nontrivial infrared fixed point, which exhibits nonanalytic scaling behavior only in the time direction. For some representatives of this class, the resistivity has a linear temperature dependence, as is the case for strange metals.

Holographic non-Fermi-liquid fixed points

Techniques arising from string theory can be used to study assemblies of strongly interacting fermions. Via this ‘holographic duality’, various strongly coupled many-body systems are solved using an auxiliary theory of gravity. Simple holographic realizations of finite density exhibit single-particle spectral functions with sharp Fermi surfaces, of a form distinct from those of the Landau theory. The self-energy is given by a correlation function in an infrared (IR) fixed-point theory that is represented by a two-dimensional anti de Sitter space (AdS2) region in the dual gravitational description. Here, we describe in detail the gravity calculation of this IR correlation function.

Holographic entanglement entropy and gravitational anomalies

A bstractWe study entanglement entropy in two-dimensional conformal field theories with a gravitational anomaly. In theories with gravity duals, this anomaly is holographically represented by a gravitational Chern-Simons term in the bulk action. We show that the anomaly broadens the Ryu-Takayanagi minimal worldline into a ribbon, and that the anomalous contribution to the CFT entanglement entropy is given by the twist in this ribbon. The entanglement functional may also be interpreted as the worldline action for a spinning particle — that is, an anyon — in three-dimensional curved spacetime. We demonstrate that the minimization of this action results in the Mathisson-Papapetrou-Dixon equations of motion for a spinning particle in three dimensions. We work out several simple examples and demonstrate agreement with CFT calculations.

Friedel oscillations and horizon charge in 1D holographic liquids

A bstractIn many-body fermionic systems at finite density correlation functions of the density operator exhibit Friedel oscillations at a wavevector that is twice the Fermi momentum. We demonstrate the existence of such Friedel oscillations in a 3d gravity dual to a compressible finite-density state in a (1+1) dimensional field theory. The bulk dynamics is provided by a Maxwell U(1) gauge theory and all the charge is behind a bulk horizon. The bulk gauge theory is compact and so there exist magnetic monopole tunneling events. We compute the effect of these monopoles on holographic density-density correlation functions and demonstrate that they cause Friedel oscillations at a wavevector that directly counts the charge behind the bulk horizon. If the magnetic monopoles are taken to saturate the bulk Dirac quantization condition then the observed Fermi momentum exactly agrees with that predicted by Luttinger’s theorem, suggesting some Fermi surface structure associated with the charged horizon. The mechanism is generic and will apply to any charged horizon in three dimensions. Along the way we clarify some aspects of the holographic interpretation of Maxwell electromagnetism in three bulk dimensions and show that perturbations about the charged BTZ black hole exhibit a hydrodynamic sound mode at low temperature.

Holography and the Coleman-Mermin-Wagner theorem

In 2+1 dimensions at finite temperature, spontaneous symmetry breaking of global symmetries is precluded by large thermal fluctuations of the order parameter. The holographic correspondence implies that analogous effects must also occur in 3+1 dimensional theories with gauged symmetries in certain curved spacetimes with horizon. By performing a one loop computation in the background of a holographic superconductor, we show that bulk quantum fluctuations wash out the classical order parameter at sufficiently large distance scales. The low temperature phase is seen to exhibit algebraic long-range order. Beyond the specific example we study, holography suggests that IR singular quantum fluctuations of the fields and geometry will play an interesting role for many 3+1 dimensional asymptotically anti-de Sitter spacetimes with planar horizon.

Emergence of oscillons in an expanding background

We consider a (1+1) dimensional scalar field theory that supports oscillons, which are localized, oscillatory, stable solutions to nonlinear equations of motion. We study this theory in an expanding background and show that oscillons now lose energy, but at a rate that is exponentially small when the expansion rate is slow. We also show numerically that a universe that starts with (almost) thermal initial conditions will cool to a final state where a significant fraction of the energy of the universe--on the order of 50%--is stored in oscillons. If this phenomenon persists in realistic models, oscillons may have cosmological consequences.

Entanglement Entropy in Warped Conformal Field Theories

A bstractWe present a detailed discussion of entanglement entropy in (1+1)-dimensional Warped Conformal Field Theories (WCFTs). We implement the Rindler method to evaluate entanglement and Renyi entropies for a single interval and along the way we interpret our results in terms of twist field correlation functions. Holographically a WCFT can be described in terms of Lower Spin Gravity, a SL (2, ℝ) × U (1) Chern-Simons theory in three dimensions. We show how to obtain the universal field theory results for entanglement in a WCFT via holography. For the geometrical description of the theory we introduce the concept of geodesic and massive point particles in the warped geometry associated to Lower Spin Gravity. In the Chern-Simons description we evaluate the appropriate Wilson line that captures the dynamics of a massive particle.