Scientific Series

I describe recent work with with Stefan Hollands that establishes a new criterion for the dynamical stability of black holes in $D \geq 4$ spacetime dimensions in general relativity with respect to axisymmetric perturbations: Dynamic stability is equivalent to the positivity of the canonical energy, $\mathcal E$, on a subspace of linearized solutions that have vanishing linearized ADM mass, momentum, and angular momentum at infinity and satisfy certain gauge conditions at the horizon.  We further show that $\mathcal E$ is related to the second order variations of mass, angular momentum, and horizon area by $\mathcal E = \delta^2 M - \sum_i \Omega_i \delta^2 J_i - (\kappa/8\pi) \delta^2 A$, thereby establishing a close connection between dynamic stability and thermodynamic stability.

Thermodynamic instability of a family of black holes need not imply dynamic instability because the perturbations towards other members of the family will not, in general, have vanishing linearized ADM mass and/or angular momentum. However, we prove that all black branes corresponding to
thermodynmically unstable black holes are dynamically unstable, as conjectured by Gubser and Mitra. We also prove that positivity of $\mathcal E$ is equivalent to the satisfaction of a ``local Penrose inequality,'' thus showing that satisfaction of this local Penrose inequality is necessary and sufficient for dynamical stability.

When a large number of quantum mechanical particles are put together and allowed to interact, various condensed matter phases emerge with macroscopic quantum properties. While conventional quantum phases like superfluids or quantum magnets can be understood as a simple collection of
single particle quantum states, recent discoveries of fractional quantum Hall or spin liquids states contain intrinsic entanglement among all the particles. To understand such unconventional phases requires unconventional methods. In this talk, I will discuss how the quantum information insights about many-body entanglement gives us a unique perspective and a powerful tool to study these
unconventional phases. In particular, starting from simple entanglement building blocks, we are able to construct new gapped quantum phases, classify all possible gapped phases in certain cases and obtain a better understanding of the structure of the phase diagram. With these progress, we expect the many-body entanglement point of view to play an important role in our effort to map the full quantum phase diagram, leading to breakthroughs in our understanding of gapless phases and phase transitions and in the development of numerical tools to simulate such systems.

Shor's algorithm can be a meaningful test for experimental quantum processing systems, when suitably realized.  I present results from a  recent implemenation of quantum factoring using trapped ion qubits, demonstrating feed-forward control, use of quantum memory during computation, and cascaded three-qubit gates.  Such capabilities are necessary ingredients for a future large-scale,
fault-tolerant quantum computing system.

Hexagon functions are a class of iterated integrals, depending on three variables (dual conformal cross ratios) which have the correct branch cut structure and other properties to describe the scattering of six gluons in planar N=4 super-Yang-Mills theory. We classify all hexagon
functions through transcendental weight five, using the coproduct for their Hopf algebra iteratively, which amounts to a set of first-order differential equations.  As an example, the three-loop remainder function is a particular weight-six hexagon function, whose symbol was determined
previously.

The differential equations can be integrated numerically for generic values of the cross ratios, or analytically in certain kinematics limits, including the near-collinear and multi-Regge
limits.  These limits allow us to impose constraints from the operator product expansion and multi-Regge factorization directly at the function level, and thereby to fix uniquely a set of Riemann-Zeta-valued constants that could not be fixed at the level of the symbol. The near-collinear limits agree precisely with recent predictions by Basso, Sever and Vieira based on integrability.  The multi-Regge limits agree with a factorization formula of Fadin and Lipatov, and determine three constants entering the impact factor at this order. We plot the three-loop remainder function for various slices of the Euclidean region of positive cross ratios, and compare it to the two-loop one.  For large ranges of the cross ratios, the ratio of the three-loop to the two-loop remainder function is relatively constant, and close to -7.

I will describe recent results obtained for N=4 superconformal field
theories in four dimensions by means of the conformal bootstrap.

This talk will be related to the content of arXiv:1304.1803, as well as
some additional work in progress.

The direct detection of gravitational waves promises to open up a new spectrum that is otherwise mostly closed to electromagnetically based astronomical observations. Detecting gravitational waves from binary black holes and neutron stars, as well as estimating their parameters, requires a sufficiently accurate prediction for the expected waveform signal. Unfortunately, the state of the art for the pillars of gravitational wave theory -- numerical relativity, the post-Newtonian approximation, and linear black hole perturbation theory -- have yet to cover accurately the entire parameter space even when taken together. In this talk, I present a new direction for systematically describing compact binaries that is valid over a potentially very large portion of the parameter space.

The approach uses high-order black hole perturbation theory in the mass ratio together with ideas and techniques borrowed from effective field theory for incorporating the physics of extended masses like spin and tidal effects. I discuss recent advances, future prospects, and potential impacts in this direction.

We show explicitly how the exact renormalization group
equation of interacting vector models in the large N limit can be
mapped into certain higher-spin equations of motion. The equations of
motion are generalized to incorporate a multiparticle extension of the
higher-spin algebra, which reflects the "multitrace" nature of the
interactions in the dual field theory from the holographic point of view.

Spins play a major role in the strong-field dynamics of
black-hole binaries and their gravitational-wave emission. By detecting spin
effects in the waveforms, existing and future gravitational-wave detectors
therefore provide a natural way to test gravity in strong-field, highly
dynamical regimes.

In the first part of my talk, I will show that the
inclusion of the spins in the gravitational templates for future space-based
detectors will permit testing scenarios for the formation and cosmological
evolution of supermassive black holes, and possibly shed light on models of
galaxy formation. In the second part, I will show that the effective-one-body
(EOB) model provides an efficient way to account for spin effects in both the
dynamics and waveforms, by combining information from post-Newtonian theory,
the self-force formalism, and numerical-relativity simulations.

While quantum measurement remains the central philosophical conundrum of quantum mechanics, it has recently grown into a respectable (read: experimental!) discipline as well.  New perspectives on measurement have grown  out of new technological possibilities, but also out of
attempts to design systems for quantum information processing, which promise to be exponentially more powerful than any possible classical computer.  I will try to give a flavour about some of these perspectives, focussing largely on a particular paradigm known as "weak measurement."
Weak measurement is a natural extension of a pragmatic view of what it means to measure something about a quantum system, yet leads to some rather surprising results.  I will describe a few examples of our recent experiments using weak measurement to probe fundamental issues in  uantum mechanics such as what the minimum disturbance due to a quantum measurement is.  I will also argue that there are regimes in which weak measurement offers a practical advantage for sensitive measurements.  

The ground-based gravitational-wave telescopes LIGO and Virgo approach the era of first detections.  Gravitational-wave observations will provide a unique probe for exploring strong-field general relativity and compact-binary astrophysics.  In this talk, I describe recent predictions regarding the distributions of black-hole and neutron-star binary mergers, and progress on solving the inverse problem of turning gravitational-wave observations into astrophysical information. I highlight some exciting recent investigations into the use of gravitational waves as tests of general relativity.

The fuzzball proposal makes a conjecture about the nature of black hole
microstates. Now, more than a decade old and including several different
philosophies and perspectives, it is especially relevant after the recent
firewall argument and ensuing debate. Over three lectures, I plan to start
with a very general discussion of the general ideas and motivations, then
review the theoretical evidence from string theory, and finally close by
discussing open questions, including the fate of a freely falling observer
as he/she passes through the black hole horizon.

The fuzzball proposal makes a conjecture about the nature of black hole
microstates. Now, more than a decade old and including several different
philosophies and perspectives, it is especially relevant after the recent
firewall argument and ensuing debate. Over three lectures, I plan to start
with a very general discussion of the general ideas and motivations, then
review the theoretical evidence from string theory, and finally close by
discussing open questions, including the fate of a freely falling observer
as he/she passes through the black hole horizon.