We use the complexity ¼ action (CA) conjecture to study the full-time dependence of holographic complexity in anisotropic black branes. We find that the time behavior of holographic complexity of anisotropic systems shares a lot of similarities with the behavior observed in isotropic systems. In particular, the holographic complexity remains constant for some initial period, and then it starts to change so that the complexity growth rate violates the Lloyd's bound at initial times, and approaches this bound from above at later times. Compared with isotropic systems at the same temperature, the anisotropy reduces the initial period in which the complexity is constant and increases the rate of change of complexity. At late times the difference between the isotropic and anisotropic results is proportional to the pressure difference in the transverse and longitudinal directions. In the case of charged anisotropic black branes, we find that the inclusion of a Maxwell boundary term is necessary to have consistent results. Moreover, the resulting complexity growth rate does not saturate the Lloyd's bound at late times.

We write down Crofton formulas — expressions that compute lengths of space- like curves in asymptotically AdS3 geometries as integrals over kinematic space — which apply when the curve and/or the background spacetime is time-dependent. Relative to their static predecessor, the time-dependent Crofton formulas display several new features, whose origin is the local null rotation symmetry of the bulk geometry. In pure AdS3 where null rotations are global symmetries, the Crofton formulas simplify and become integrals over the null planes, which intersect the bulk curve.

We study the propagation of a neutrino in a medium that consists of two or more thermal backgrounds of electrons and nucleons moving with some relative velocity, in the presence of a static and homogeneous electromagnetic field. We calculate the neutrino self-energy and dispersion relation using the linear thermal Schwinger propagator, we give the formulas for the dispersion relation and discuss general features of the results obtained, in particular the effects of the stream contributions. As a specific example we discuss in some detail the case of a magnetized two-stream electron, i.e., two electron backgrounds with a relative velocity v in the presence of a magnetic field. For a neutrino propagating with momentum k, in the presence of the stream the neutrino dispersion relation acquires an anisotropic contribution of the formk · v in addition to the well known termk · B, as well as an additional contribution proportional to B · v. We consider the contribution from a nucleon stream background as an example of other possible stream backgrounds, and comment on possible generalizations to take into account the effects of inhomogeneous fields. We explain why a term of the formk · (v × B) does not appear in the dispersion relation in the constant field case, while a term of similar form can appear in the presence of an inhomogeneous field involving its gradient.

No abstract

There is some tension between two well-known ideas in holography. On the one hand, subregion duality asserts that the reduced density matrix associated with a limited region of the boundary theory is dual to a correspondingly limited region in the bulk, known as the entanglement wedge. On the other hand, correlators that in the boundary theory can be computed solely with that density matrix are calculated in the bulk via the GKPW or BDHM prescriptions, which require input from beyond the entanglement wedge. We show that this tension is resolved by recognizing that the reduced state is only fully identified when the entanglement wedge is supplemented with a specific infrared boundary action, associated with an end-of-the-world brane. This action is obtained by coarse-graining through a variant of Wilsonian integration, a procedure that we call holographic rememorization, which can also be applied to define other reduced density or transition matrices, as well as more general reduced partition functions. We find an interesting connection with AdS/BCFT, and, in this context, we are led to a simple example of an equivalence between an ensemble of theories and a single theory, as discussed in recent studies of the black hole information problem.