Bridging the static patches: de Sitter holography and entanglement

In the context of de Sitter static-patch holography, two prescriptions have been put forward for holographic entanglement entropy computations, the monolayer and bilayer proposals. In this paper, we reformulate both prescriptions in a covariant way and extend them to include quantum corrections. We argue that the bilayer proposal is self-consistent, while the monolayer proposal exhibits contradictory behavior. In fact, the bilayer proposal leads to a stronger holographic description, in which the full spacetime is encoded on two screens at the cosmological horizons. At the classical level, we find large degeneracies of minimal extremal homologous surfaces, localized at the horizons, which can be lifted by quantum corrections. The entanglement wedges of subregions of the screens exhibit non-trivial behaviors, hinting at the existence of interesting phase transitions and non-locality in the holographic theory. In particular, while each screen encodes its corresponding static patch, we show that the entanglement wedge of the screen with the larger quantum area extends and covers the causal diamond between the screens, with a phase transition occurring when the quantum areas of the screens become equal. We argue that the capacity of the screens to encode the region between them is lost, when these are pushed further in the static patches of the observers and placed on stretched horizons.Comment: 83 pages, 11 figures. Published versio

Closed FRW holography: A time-dependent ER=EPR realization

We extend a recent de Sitter holographic proposal and entanglement entropy prescription to generic closed FRW cosmologies in arbitrary dimensions, and propose that for large classes of bouncing and Big Bang/Big Crunch cosmologies, the full spacetime can be encoded holographically on two holographic screens, associated to two antipodal observers. In the expanding phase, the two screens lie at the apparent horizons. In the contracting phase, there is an infinite number of possible trajectories of the holographic screens, which can be grouped in equivalence classes. In each class the effective holographic theory can be derived from a pair of ``parent'' screens on the apparent horizons. A number of cases including moduli-dominated cosmologies escape our discussion, and it is expected that two antipodal observers and their associated screens do not suffice to reconstruct these cosmologies. The leading contributions to the entanglement entropy between the screens arise from a minimal extremal trapped or anti-trapped surface lying in the region between them. This picture entails a time-dependent realization of the ER=EPR conjecture, where an effective geometrical bridge connecting the screens via the minimal extremal surface emerges from entanglement. For the Big Crunch contracting cases, the screens disentangle and the geometrical bridge closes off when the minimal extremal trapped sphere hits the Big Crunch singularity at a finite time before the collapse of the Universe. Semiclassical, thermal corrections are incorporated in the cases of radiation-dominated cosmologies.Comment: 72 pages, 16 figures, 3 appendice

Massless D-strings and moduli stabilization in type I cosmology

We consider the cosmological evolution induced by the free energy F of a gas of maximally supersymmetric heterotic strings at finite temperature and weak coupling in dimension D>=4. We show that F, which plays the role of an effective potential, has minima associated to enhanced gauge symmetries, where all internal moduli can be attracted and dynamically stabilized. Using the fact that the heterotic/type I S-duality remains valid at finite temperature and can be applied at each instant of a quasi-static evolution, we find in the dual type I cosmology that all internal NS-NS and RR moduli in the closed string sector and the Wilson lines in the open string sector can be stabilized. For the special case of D=6, the internal volume modulus remains a flat direction, while the dilaton is stabilized. An essential role is played by light D-string modes wrapping the internal manifold and whose contribution to the free energy cannot be omitted, even when the type I string is at weak coupling. As a result, the order of magnitude of the internal radii expectation values on the type I side is (lambda_I alpha')^{1/2}, where lambda_I is the ten-dimensional string coupling. The non-perturbative corrections to the type I free energy can alternatively be described as effects of "thermal E1-instantons", whose worldsheets wrap the compact Euclidean time cycle.Comment: 39 pages, 1 figur

Inflationary de Sitter solutions from superstrings

In the framework of superstring compactifications with N=1 supersymmetry spontaneously broken, (by either geometrical fluxes, branes or else), we show the existence of new inflationary solutions. The time-trajectory of the scale factor of the metric a, the supersymmetry breaking scale m=m(Phi) and the temperature T are such that am and aT remain constant. These solutions request the presence of special moduli-fields: i) The universal "no-scale-modulus" Phi, which appears in all N=1 effective supergravity theories and defines the supersymmetry breaking scale m(Phi). ii) The modulus Phi_s, which appears in a very large class of string compactifications and has a Phi-dependent kinetic term. During the time evolution, a^4 rho_s remains constant as well, (rho_s being the energy density induced by the motion of Phi_s). The cosmological term Lambda(am), the curvature term k(am, aT) and the radiation term c_R=a^4 rho are dynamically generated in a controllable way by radiative and temperature corrections; they are effectively constant during the time evolution. Depending on Lambda, k and c_R, either a first or second order phase transition can occur in the cosmological scenario. In the first case, an instantonic Euclidean solution exists and connects via tunneling the inflationary evolution to another cosmological branch. The latter starts with a big bang and, in the case the transition does not occur, ends with a big crunch. In the second case, the big bang and the inflationary phase are smoothly connected.Comment: 37 pages, 4 eps figure

Thermal duality and non-singular cosmology in d-dimensional superstrings

We are presenting the basic ingredients of a stringy mechanism able to resolve both the Hagedorn instabilities of finite temperature superstrings as well as the initial singularity of the induced cosmology in arbitrary dimensions. These are shown to be generic in a large class of (4,0) type II superstring vacua, where non-trivial "gravito-magnetic" fluxes lift the Hagedorn instabilities of the thermal ensemble and the temperature duality symmetry is restored. This symmetry implies a universal maximal critical temperature. In all such models there are three characteristic regimes, each with a distinct effective field theory description: Two dual asymptotically cold regimes associated with the light thermal momentum and light thermal winding states, and the intermediate regime where additional massless thermal states appear. The partition function exhibits a conical structure as a function of the thermal modulus, irrespective of the space-time dimension. Thanks to asymptotic right-moving supersymmetry, the genus-1 partition function is well-approximated by that of massless thermal radiation in all of the three effective field theory regimes. The resulting time-evolution describes a bouncing cosmology connecting, via spacelike branes, a contracting thermal "winding" Universe to an expanding thermal "momentum" Universe, free of any essential curvature singularities. The string coupling remains perturbative throughout the cosmological evolution. Bouncing cosmologies are presented for both zero and negative spatial curvature.Comment: 39+1 pages, 2 figure

Induced superstring cosmologies and moduli stabilization

We extend the analysis of the recently obtained stringy cosmological solutions induced by thermal and quantum effects, once space-time supersymmetry is spontaneously broken by geometrical fluxes. Cases in which more than one modulus participating in the supersymmetry breaking mechanism are investigated. The free energy is obtained at the full string level. In the intermediate cosmological region where the temperature and the supersymmetry breaking scale are sufficiently smaller than the Hagedorn temperature, the quantum and thermal corrections are under control and calculable. The reason is that the contributions to the effective potential of the moduli that are not participating in the supersymmetry breaking are exponentially suppressed. The backreaction on the initially flat background results in many cases into cosmological evolutions, where the dynamics of all complex structure moduli is frozen. The solutions describe effectively a radiation dominated era, where thermal effects are never negligible, even if the temperature tends to zero at late times. We analyze several types of supersymmetry breaking patterns and examine the stability of the corresponding radiation era.Comment: 37 pages, 5 figure

Resolution of Hagedorn singularity in superstrings with gravito-magnetic fluxes

We consider closed type II and orientifold backgrounds where supersymmetry is spontaneously broken by asymmetric geometrical fluxes. We show that these can be used to describe thermal ensembles with chemical potentials associated to "gravito-magnetic" fluxes. The thermal free energy is computed at the one-loop string level, and it is shown to be free of the usual Hagedorn-like instabilities for a certain choice of the chemical potentials. In the closed string gravitational sector, as well as in the open string matter sector of the proposed orientifold construction, the free energy turns out to have "Temperature duality" symmetry, ${\cal F}(T/T_H)={T^2\over T_H^2} {\cal F}(T_H/T)$, which requires interchanging the space-time spinor representations $S\leftrightarrow C$. For small temperatures, $T\to 0$, the anti-spinor $C$ decouples from the spectrum while for large temperatures, $T\to \infty$, the spinor $S$ decouples. In both limits the free energy vanishes, as we recover a conventional type II superstring theory. At the self dual point $T=T_H$, the thermal spectra of $S$ and $C$ are identical. Moreover, there are extra massless scalars in the adjoint representation of an SO(4) non-abelian gauge symmetry in the closed-string sector, and open-string massless states charged simultaneously under both the Chan-Paton and the closed-string SO(4) gauge group.Comment: LaTeX, 1+23 pages. v2 Section 2.1 expanded. Misprints corrected. To appear in Nuclear Physics