Dimensional reduction from entanglement in Minkowski space

Using a quantum field theoretic setting, we present evidence for dimensional reduction of any sub-volume of Minkowksi space. First, we show that correlation functions of a class of operators restricted to a sub-volume of D-dimensional Minkowski space scale as its surface area. A simple example of such area scaling is provided by the energy fluctuations of a free massless quantum field in its vacuum state. This is reminiscent of area scaling of entanglement entropy but applies to quantum expectation values in a pure state, rather than to statistical averages over a mixed state. We then show, in a specific case, that fluctuations in the bulk have a lower-dimensional representation in terms of a boundary theory at high temperature.Comment: 9 pages, changes to presentation, some content corrections, version published in JHE

Comments on No-Hair Theorems and Stabilty of Blackholes

In the light of recent blackhole solutions inspired by string theory, we review some old statements on field theoretic hair on blackholes. We also discuss some stability issues. In particular we argue that the two dimensional string blackhole solution is semi-classically stable while the naked singularity is unstable to tachyon fluctuations. Finally we comment on the relation between the linear dilaton theory and the $2d$ blackhole solution.Comment: 14 page

Thermodynamics and area in Minkowski space: Heat capacity of entanglement

Tracing over the degrees of freedom inside (or outside) a sub-volume V of Minkowski space in a given quantum state |psi>, results in a statistical ensemble described by a density matrix rho. This enables one to relate quantum fluctuations in V when in the state |psi>, to statistical fluctuations in the ensemble described by rho. These fluctuations scale linearly with the surface area of V. If V is half of space, then rho is the density matrix of a canonical ensemble in Rindler space. This enables us to `derive' area scaling of thermodynamic quantities in Rindler space from area scaling of quantum fluctuations in half of Minkowski space. When considering shapes other than half of Minkowski space, even though area scaling persists, rho does not have an interpretation as a density matrix of a canonical ensemble in a curved, or geometrically non-trivial, background.Comment: 17 page

Effective Potentials for Light Moduli

We examine recent work on compactifications of string theory with fluxes, where effective potentials for light moduli have been derived after integrating out moduli that are assumed to be heavy at the classical level, and then adding non-perturbative (NP) corrections to the superpotential. We find that this two stage procedure is not valid and that the correct potential has additional terms. Althought this does not affect the conclusion of Kachru et al (KKLT) that the Kaehler moduli may be stabilized by NP effects, it can affect the detailed physics. In particular it is possible to get metastable dS minima without adding uplifting terms.Comment: Minor revisions, References added, Version to be published in PLB, 14 pages 3 figure

Moduli potentials in string compactifications with fluxes: mapping the Discretuum

We find de Sitter and flat space solutions with all moduli stabilized in four dimensional supergravity theories derived from the heterotic and type II string theories, and explain how all the previously known obstacles to finding such solutions can be removed. Further, we argue that if the compact manifold allows a large enough space of discrete topological choices then it is possible to tune the parameters of the four dimensional supergravity such that a hierarchy is created and the solutions lie in the outer region of moduli space in which the compact volume is large in string units, the string coupling is weak, and string perturbation theory is valid. We show that at least two light chiral superfields are required for this scenario to work, however, one field is sufficient to obtain a minimum with an acceptably small and negative cosmological constant. We discuss cosmological issues of the scenario and the possible role of anthropic considerations in choosing the vacuum of the theory. We conclude that the most likely stable vacuua are in or near the central region of moduli space where string perturbation theory is not strictly valid, and that anthropic considerations cannot help much in choosing a vacuum.Comment: 34 pages, no figure

Entanglement Interpretation of Black Hole Entropy in String Theory

We show that the entropy resulting from the counting of microstates of non extremal black holes using field theory duals of string theories can be interpreted as arising from entanglement. The conditions for making such an interpretation consistent are discussed. First, we interpret the entropy (and thermodynamics) of spacetimes with non degenerate, bifurcating Killing horizons as arising from entanglement. We use a path integral method to define the Hartle-Hawking vacuum state in such spacetimes and discuss explicitly its entangled nature and its relation to the geometry. If string theory on such spacetimes has a field theory dual, then, in the low-energy, weak coupling limit, the field theory state that is dual to the Hartle-Hawking state is a thermofield double state. This allows the comparison of the entanglement entropy with the entropy of the field theory dual, and thus, with the Bekenstein-Hawking entropy of the black hole. As an example, we discuss in detail the case of the five dimensional anti-de Sitter, black hole spacetime

T and S dualities and The cosmological evolution of the dilaton and the scale factors

Cosmologically stabilizing radion along with the dilaton is one of the major concerns of low energy string theory. One can hope that T and S dualities can provide a plausible answer. In this work we study the impact of S and T duality invariances on dilaton gravity. We have shown various instances where physically interesting models arise as a result of imposing the mentioned invariances. In particular S duality has a very privileged effect in that the dilaton equations partially decouple from the evolution of the scale factors. This makes it easy to understand the general rules for the stabilization of the dilaton. We also show that certain T duality invariant actions become S duality invariance compatible. That is they mimic S duality when extra dimensions stabilize.Comment: Corrected a misleading interpretation of the S duality transformation and a wrong comment on d=10. I thank A.Kaya for pointing this out to me in time. So the new version is dealing with d=10 only. Added references and corrected some typos. Minor re-editing. Omitted a section for elaboration in a further study. Corrected further typo

String Phenomenology and the Cosmological Constant

It is argued that classical string solutions should not be fine tuned to have a positive cosmological constant (CC) at the observed size, since even the quantum corrections from standard model effects will completely negate any classical string theory solution with such a CC. In fact it is even possible that there is no need at all for any ad hoc uplifting term in the potential since these quantum effects may well take care of this. Correspondingly any calculation of the parameters of the MSSM has to be rethought to take into account the evolution of the CC. This considerably complicates the issue since the initial conditions for RG evolution of these parameters are determined by the final condition on the CC! The Anthropic Principle is of no help in addressing these issues.Comment: Added equation (20) clarifying usual assumption behind calculations of soft terms. Version published in PL

Brane World Scenarios and the Cosmological Constant

Brane world scenarios offer a way of ensuring that a Poincare invariant four dimensional world can emerge, without fine tuning, as a solution to the equations of motion of an effective action. We discuss the different ways in which this happens, and point out that the underlying reason is that there is a contribution to the effective cosmological constant which is a constant of integration, that maybe adjusted to ensure a flat space solution. Basically this is an old idea revived in a new context and we speculate that there may be string scenarios that provide a concrete realization of it. Finally we discuss to what extent this is a solution to the cosmological constant problem.Comment: Expanded discussion of the brane world scenario in type IIB. Version to be published in Nuclear Physics

Resonant structure of space-time of early universe

A new fully quantum method describing penetration of packet from internal well outside with its tunneling through the barrier of arbitrary shape used in problems of quantum cosmology, is presented. The method allows to determine amplitudes of wave function, penetrability $T_{\rm bar}$ and reflection $R_{\rm bar}$ relatively the barrier (accuracy of the method: $|T_{\rm bar}+R_{\rm bar}-1| < 1 \cdot 10^{-15}$), coefficient of penetration (i.e. probability of the packet to penetrate from the internal well outside with its tunneling), coefficient of oscillations (describing oscillating behavior of the packet inside the internal well). Using the method, evolution of universe in the closed Friedmann--Robertson--Walker model with quantization in presence of positive cosmological constant, radiation and component of generalize Chaplygin gas is studied. It is established (for the first time): (1) oscillating dependence of the penetrability on localization of start of the packet; (2) presence of resonant values of energy of radiation $E_{\rm rad}$, at which the coefficient of penetration increases strongly. From analysis of these results it follows: (1) necessity to introduce initial condition into both non-stationary, and stationary quantum models; (2) presence of some definite values for the scale factor $a$, where start of expansion of universe is the most probable; (3) during expansion of universe in the initial stage its radius is changed not continuously, but passes consequently through definite discrete values and tends to continuous spectrum in latter time.Comment: 18 pages, 14 figures, 4 table