We study the entanglement between soft and hard particles produced in generic scattering processes in QED. The reduced density matrix for the hard particles, obtained via tracing over the entire spectrum of soft photons, is shown to have a large eige
nvalue, which governs the behavior of the Renyi entropies and of the non-analytic part of the entanglement entropy at low orders in perturbation theory. The leading perturbative entanglement entropy is logarithmically IR divergent. The coefficient of the IR divergence exhibits certain universality properties, irrespectively of the dressing of the asymptotic charged particles and the detailed properties of the initial state. In a certain kinematical limit, the coefficient is proportional to the cusp anomalous dimension in QED. For Fock basis computations associated with two-electron scattering, we derive an exact expression for the large eigenvalue of the density matrix in terms of hard scattering amplitudes, which is valid at any finite order in perturbation theory. As a result, the IR logarithmic divergences appearing in the expressions for the Renyi and entanglement entropies persist at any finite order of the perturbative expansion. To all orders, however, the IR logarithmic divergences exponentiate, rendering the large eigenvalue of the density matrix IR finite. The all-orders Renyi entropies (per unit time, per particle flux), which are shown to be proportional to the total inclusive cross-section in the initial state, are also free of IR divergences. The entanglement entropy, on the other hand, retains non-analytic, logarithmic behavior with respect to the size of the box (which provides the IR cutoff) even to all orders in perturbation theory.
We consider scattering of Faddeev-Kulish electrons in QED and study the entanglement between the hard and soft particles in the final state at the perturbative level. The soft photon spectrum naturally splits into two parts: i) soft photons with ener
gies less than a characteristic infrared scale $E_d$ present in the clouds accompanying the asymptotic charged particles, and ii) sufficiently low energy photons with energies greater than $E_d$, comprising the soft part of the emitted radiation. We construct the density matrix associated with tracing over the radiative soft photons and calculate the entanglement entropy perturbatively. We find that the entanglement entropy is free of any infrared divergences order by order in perturbation theory. On the other hand infrared divergences in the perturbative expansion for the entanglement entropy appear upon tracing over the entire spectrum of soft photons, including those in the clouds. To leading order the entanglement entropy is set by the square of the Fock basis amplitude for real single soft photon emission, which leads to a logarithmic infrared divergence when integrated over the photon momentum. We argue that the infrared divergences in the entanglement entropy (per particle flux per unit time) in this latter case persist to all orders in perturbation theory in the infinite volume limit.
We define a three-dimensional quantum theory of gravity as the holographic dual of the Liouville conformal field theory. The theory is consistent and unitary by definition. The corresponding theory of gravity with negative cosmological constant has p
eculiar properties. The quantum theory has no normalisable AdS3 vacuum. The model contains primary black holes with zero spin. All states can be interpreted as black holes dressed with boundary gravitons. There is a unique universal interaction between these states consistent with unitarity and the conformal symmetry of the model. This theory of gravity, though conceptually isolated from other models of quantum gravity, is worth scrutinising.
We show that the Quantum Hall Soliton constructed in cite{giantbob} is stable under small perturbations. We find that creating quasiparticles actually lowers the energy of the system, and discuss whether this indicates an instability on the time scales relevant to the problem.
There is substantial evidence that string theory on AdS_5 x S_5 is a holographic theory in which the number of degrees of freedom scales as the area of the boundary in Planck units. Precisely how the theory can describe bulk physics using only surfac
e degrees of freedom is not well understood. A particularly paradoxical situation involves an event deep in the interior of the bulk space. The event must be recorded in the (Schroedinger Picture) state vector of the boundary theory long before a signal, such as a gravitational wave, can propagate from the event to the boundary. In a previous paper with Polchinski, we argued that the precursor operators which carry information stored in the wave during the time when it vanishes in a neighborhood of the boundary are necessarily non-local. In this paper we argue that the precursors cannot be products of local gauge invariant operators such as the energy momentum tensor. In fact gauge theories have a class of intrinsically non-local operators which cannot be built from local gauge invariant objects. These are the Wilson loops. We show that the precursors can be identified with Wilson loops whose spatial size is dictated by the UV-IR connection.
