In this note, we construct simple stochastic toy models for holographic gauge theories in which distributions of energy on a collection of sites evolve by a master equation with some specified transition rates. We build in only energy conservation, l
ocality, and the standard thermodynamic requirement that all states with a given energy are equally likely in equilibrium. In these models, we investigate the qualitative behavior of the dynamics of the energy distributions for different choices of the density of states for the individual sites. For typical field theory densities of states (log(rho(E)) ~ E^{alpha<1}), the model gives diffusive behavior in which initially localized distributions of energy spread out relatively quickly. For large N gauge theories with gravitational duals, the density of states for a finite volume of field theory degrees of freedom typically includes a Hagedorn regime (log(rho(E)) ~ E). We find that this gives rise to a trapping of energy in subsets of degrees of freedom for parametrically long time scales before the energy leaks away. We speculate that this Hagedorn trapping may be part of a holographic explanation for long-lived gravitational bound states (black holes) in gravitational theories.
Loop corrections to observables in slow-roll inflation are found to diverge no worse than powers of the log of the scale factor, extending Weinbergs theorem to quasi-single field inflation models. Demanding perturbation theory be valid during primord
ial inflation leads to constraints on the effective lagrangian. This leads to some interesting constraints and coincidences on the landscape of inflationary vacua.
The postulates of black hole complementarity do not imply a firewall for infalling observers at a black hole horizon. The dynamics of the stretched horizon, that scrambles and re-emits information, determines whether infalling observers experience an
ything out of the ordinary when entering a large black hole. In particular, there is no firewall if the stretched horizon degrees of freedom retain information for a time of order the black hole scrambling time.
The long wavelength physics in a de Sitter region depends on the initial quantum state. While such long wavelength physics is under control for massive fields near the Hartle-Hawking vacuum state, such initial states make unnatural assumptions about
initial data outside the region of causal contact of a local observer. We argue that a reasonable approximation to a maximum entropy state, one that makes minimal assumptions outside an observers horizon volume, is one where a cutoff is placed on a surface bounded by timelike geodesics, just outside the horizon. For sufficiently early times, such a cutoff induces secular logarithmic divergences with the expansion of the region. For massive fields, these effects sum to finite corrections at sufficiently late times. The difference between the cutoff correlators and Hartle-Hawking correlators provides a measure of the theoretical uncertainty due to lack of knowledge of the initial state in causally disconnected regions. These differences are negligible for primordial inflation, but can become significant during epochs with very long-lived de Sitter regions, such as we may be entering now.
We propose a unitary toy model of black hole evaporation, in which the entanglement between the interior and exterior degrees of freedom vanishes at late times. Our model possesses the information-free property and satisfies the niceness conditions d
iscussed in the literature. A key feature of the model is that the Hilbert space of black hole internal states contains a vacuum state corresponding to the completely evaporated black hole, which can be reached from any initial state via the Hawking process. Our model suggests a novel quantum cosmological way in which information can get out of an evaporating black hole.
We study tunneling between vacua in multi-dimensional field spaces. Working in the strict thin wall approximation, we find that the conventional instantons for false vacuum decay develop a new vanishing eigenvalue in their fluctuation determinant, ar
ising from decorations of the nucleating bubble wall with small spots of the additional vacua. Naively, this would suggest that the presence of additional vacua in field space leads to a substantial enhancement of the nucleation rate. However, we argue that this potential enhancement is regulated away by the finite thickness of physical bubble wall intersections. We then discuss novel saddle points of the thin wall action that, in some regimes of parameter space, have the potential to destabilize the conventional instantons for false vacuum decay.
We predict the polarization of cosmic microwave background (CMB) photons that results from a cosmic bubble collision. The polarization is purely E-mode, symmetric around the axis pointing towards the collision bubble, and has several salient features
in its radial dependence that can help distinguish it from a more conventional explanation for unusually cold or hot features in the CMB sky. The anomalous cold spot detected by the Wilkinson Microwave Anisotropy Probe (WMAP) satellite is a candidate for a feature produced by such a collision, and the Planck satellite and other proposed surveys will measure the polarization on it in the near future. The detection of such a collision would provide compelling evidence for the string theory landscape.
We study large scale structure in the cosmology of Coleman-de Luccia bubble collisions. Within a set of controlled approximations we calculate the effects on galaxy motion seen from inside a bubble which has undergone such a collision. We find that g
enerically bubble collisions lead to a coherent bulk flow of galaxies on some part of our sky, the details of which depend on the initial conditions of the collision and redshift to the galaxy in question. With other parameters held fixed the effects weaken as the amount of inflation inside our bubble grows, but can produce measurable flows past the number of efolds required to solve the flatness and horizon problems.
Recently Ooguri and Yamazaki proposed a statistical model of melting crystals to count BPS bound states of certain D-brane configurations on toric Calabi--Yau manifolds [arXiv:0811.2801]. This construction relied on a set of consistency conditions on
the corresponding brane tiling, and in this note I show that these conditions are satisfied for any physical brane tiling; they follow from the conformality of the low energy field theory on the D-branes. As a byproduct I also provide a simple direct proof that any physical brane tiling has a perfect matching.
