Does Complexity Equal Anything?

We present a new infinite class of gravitational observables in asymptotically anti-de Sitter space living on codimension-one slices of the geometry, the most famous of which is the volume of the maximal slice. We show that these observables display universal features for the thermofield-double state: they grow linearly in time at late times and reproduce the switchback effect in shock wave geometries. We argue that any member of this class of observables is an equally viable candidate as the extremal volume for a gravitational dual of complexity.

First Law of Holographic Complexity.

We investigate the variation of holographic complexity for two nearby target states. Based on Nielsen's geometric approach, we find the variation only depends on the end point of the optimal trajectory, a result which we designate the first law of complexity. As an example, we examine the complexity=action conjecture when the anti-de Sitter vacuum is perturbed by a scalar field excitation, which corresponds to a coherent state. Remarkably, the gravitational contributions completely cancel and the final variation reduces to a boundary term coming entirely from the scalar field action. Hence, the null boundary of Wheeler-DeWitt patch appears to act like the "end of the quantum circuit".

Holographic de Sitter Geometry from Entanglement in Conformal Field Theory.

We demonstrate that, for general conformal field theories (CFTs), the entanglement for small perturbations of the vacuum is organized in a novel holographic way. For spherical entangling regions in a constant time slice, perturbations in the entanglement entropy are solutions of a Klein-Gordon equation in an auxiliary de Sitter (dS) spacetime. The role of the emergent timelike direction in dS spacetime is played by the size of the entangling sphere. For CFTs with extra conserved charges, e.g., higher-spin charges, we show that each charge gives rise to a separate dynamical scalar field in dS spacetime.

Universality of Corner Entanglement in Conformal Field Theories.

We study the contribution to the entanglement entropy of (2+1)-dimensional conformal field theories (CFTs) coming from a sharp corner in the entangling surface. This contribution is encoded in a function a(θ) of the corner opening angle, and was recently proposed as a measure of the degrees of freedom in the underlying CFT. We show that the ratio a(θ)/C(T), where C(T) is the central charge in the stress tensor correlator, is an almost universal quantity for a broad class of theories including various higher-curvature holographic models, free scalars, and fermions, and Wilson-Fisher fixed points of the O(N) models with N=1,2,3. Strikingly, the agreement between these different theories becomes exact in the limit θ→π, where the entangling surface approaches a smooth curve. We thus conjecture that the corresponding ratio is universal for general CFTs in three dimensions.

Equilibration Rates in a Strongly Coupled Nonconformal Quark-Gluon Plasma.

We initiate the study of equilibration rates of strongly coupled quark-gluon plasmas in the absence of conformal symmetry. We primarily consider a supersymmetric mass deformation within N=2^{*} gauge theory and use holography to compute quasinormal modes of a variety of scalar operators, as well as the energy-momentum tensor. In each case, the lowest quasinormal frequency, which provides an approximate upper bound on the thermalization time, is proportional to temperature, up to a prefactor with only a mild temperature dependence. We find similar behavior in other holographic plasmas, where the model contains an additional scale beyond the temperature. Hence, our study suggests that the thermalization time is generically set by the temperature, irrespective of any other scales, in strongly coupled gauge theories.

Universal scaling in fast quantum quenches in conformal field theories.

We study the time evolution of a conformal field theory deformed by a relevant operator under a smooth but fast quantum quench which brings it to the conformal point. We argue that when the quench time scale δt is small compared to the scale set by the relevant coupling, the expectation value of the quenched operator scales universally as δλ/δt(2Δ-d), where δλ is the quench amplitude. This growth is further enhanced by a logarithmic factor in even dimensions. We present explicit results for free scalar and fermionic field theories, supported by an analytic understanding of the leading contribution for fast quenches. Our results suggest that this scaling result, first found in holography, is in fact quite general. Our considerations also show that this limit of fast smooth quenches is quite different from an instantaneous quench from one time-independent Hamiltonian to another, where the state at the time of the quench serves as an initial condition for subsequent evolution with the final Hamiltonian.

Universality of abrupt holographic quenches.

We make an analytic investigation of rapid quenches of relevant operators in d-dimensional holographic conformal field theories, which admit a dual gravity description. We uncover a universal scaling behavior in the response of the system, which depends only on the conformal dimension of the quenched operator in the vicinity of the ultraviolet fixed point of the theory. Unless the amplitude of the quench is scaled appropriately, the work done on a system during the quench diverges in the limit of abrupt quenches for operators with dimension (d/2)≤Δ

Viscosity bound and causality violation.

In recent work we showed that, for a class of conformal field theories (CFT) with Gauss-Bonnet gravity dual, the shear viscosity to entropy density ratio, eta/s, could violate the conjectured Kovtun-Starinets-Son viscosity bound, eta/s > or = 1/4 pi. In this Letter we argue, in the context of the same model, that tuning eta/s below (16/25)(1/4 pi) induces microcausality violation in the CFT, rendering the theory inconsistent. This is a concrete example in which inconsistency of a theory and a lower bound on viscosity are correlated, supporting the idea of a possible universal lower bound on eta/s for all consistent theories.

Holographic viscosity of fundamental matter.

A holographic dual of a finite-temperature SU(Nc) gauge theory with a small number of flavors Nf< or =1/4pi. Given the known results for the entropy density, the contribution of the fundamental matter eta fund is therefore enhanced at strong 't Hooft coupling lambda; for example, eta fund approximately lambda NcNfT3 in four dimensions. Other transport coefficients are analogously enhanced. These results hold with or without a baryon number chemical potential.

Holographic phase transitions with fundamental matter.

The holographic dual of a finite-temperature gauge theory with a small number of flavors typically contains D-brane probes in a black hole background. At low temperature, the branes sit outside the black hole and the meson spectrum is discrete and possesses a mass gap. As the temperature increases, the branes approach a critical solution. Eventually, they fall into the horizon and a phase transition occurs. In the new phase, the meson spectrum is continuous and gapless. At large Nc and large 't Hooft coupling, we show that this phase transition is always first order. In confining theories with heavy quarks, it occurs above the deconfinement transition for the glue.

Ultraviolet modifications of dispersion relations in effective field theory.

The existence of a fundamental ultraviolet scale, such as the Planck scale, may lead to modifications of the dispersion relations for particles at high energies in some scenarios of quantum gravity. We apply effective field theory to this problem and identify dimension-5 operators that do not mix with dimensions 3 and 4 and lead to cubic modifications of dispersion relations for scalars, fermions, and vector particles. Further we show that, for electrons, photons and light quarks, clock comparison experiments bound these operators at 10(-5)/M(Pl).