De Sitter universes and the emerging landscape in string theory

We discuss a recent proposal to construct de Sitter vacua in string theory. It is based on flux compactifications in string theory where all the moduli are stabilised and supersymmetry is broken with control. The resulting picture is that of a complicated landscape with many vacua of widely varying values for the cosmological constant.     

Heterotic strings on homogeneous spaces

We construct heterotic string backgrounds corresponding to families of homogeneous spaces as exact conformal field theories. They contain left cosets of compact groups by their maximal tori supported by NS‐NS 2‐forms and gauge field fluxes. We give the general formalism and modular‐invariant partition functions, then we consider some examples such as SU (2)/U (1) ~ S² (already described in a previous paper) and the SU (3)/U(1)² flag space. As an application we construct new supersymmetric string vacua with magnetic fluxes and a linear dilaton.     

A method of deforming G-structures

We consider deformations of $G$-structures via the right action on the frame bundle in a base-point-dependent manner. We investigate which of these deformations again lead to $G$-structures and in which cases the original and the deformed $G$-structures define the same instantons. Further, we construct a bijection from connections compatible with the original $G$-structure to those compatible with the deformed $G$-structure and investigate the change of intrinsic torsion under the aforementioned deformations. Finally, we consider several examples.     

Half‐Maximal Supersymmetry from Exceptional Field Theory

We study ‐dimensional half‐maximal flux backgrounds using exceptional field theory. We define the relevant generalised structures and also find the integrability conditions which give warped half‐maximal Minkowski_D and AdS_D vacua. We then show how to obtain consistent truncations of type II / 11‐dimensional SUGRA which break half the supersymmetry. Such truncations can be defined on backgrounds admitting exceptional generalised structures, where , and N is the number of vector multiplets obtained in the lower‐dimensional theory. Our procedure yields the most general embedding tensors satisfying the linear constraint of half‐maximal gauged SUGRA. We use this to prove that all half‐maximal warped AdS_D and Minkowski_D vacua of type II / 11‐dimensional SUGRA admit a consistent truncation keeping only the gravitational supermultiplet. We also show to obtain heterotic double field theory from exceptional field theory and comment on the M‐theory / heterotic duality. In five dimensions, we find a new SO(5, N ) double field theory with a ‐dimensional extended space. Its section condition has one solution corresponding to 10‐dimensional supergravity and another yielding six‐dimensional SUGRA.     

A radiating charge embedded in a De Sitter universe

An exact solution of the Einstein-Maxwell theory is presented. The solution represents the metric of a radiating charged particle embedded in a de Sitter universe.     

Gravitational law and spinning electron equation in a De Sitter symmetric space

A gravitational law is proposed on a De Sitter covariant space. Dirac's De Sitter covariant spinning electron equation is generalized to the presence of gravitational fields. The resulting equation differs from the generally covariant Dirac equation by a mass renormalization. The last result is a generalization of that of Gürsey and Lee [2] in case of the homogenous De Sitter metric, and it gives a wider outlook on the significance of this result from the point of view of gauge theory.Dedicated to Achille Papapetrou on the occasion of his retirement.     

Quantum de Sitter algebra and some possible applications in cosmology

I summarize results recently obtained in collaboration with Amelino-Camelia, Bruno and Mandanici (preprint University of Rome “La Sapienza”, August, 2005) that concern an analysis of the path of a massless particle in a q-de Sitter space-time and an approximation scheme suitable for the corresponding analysis in a quantum FRW Universe. On the basis of some arguments in the quantum-gravity literature, the q deformation parameter is assumed to depend on both the Planck scale and the curvature, leading to results that are significantly different from those of other studies of Planck-scale effects in cosmology, where the possibility of an interplay between curvature and Planck scale was ignored. Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

Microcanonical ensemble study of a classical fluid of hard rods under gravity

The study of a system of hard rods in a box of finite length in the presence of a uniform gravitational field is made by means of the microcanonical ensemble. Explicit expressions are derived for the phase volume and the density of states, the primary functions of this ensemble. Related statistical quantities are reported, such as the entropy, the temperature, the heat capacity and the forces exerted on the fluid by the bottom and top walls. The microcanonical number density and higher order molecular distribution functions are also derived. Received: 7 April 1998 / Received in final form: 20 July 1998 / Accepted: 28 July 1998     

A New Solution with Torsion in Model of dS Gauge Theory of Gravity

A new static de Sitter solution with torsion in the model of de Sitter gauge theory of gravity is obtained. The torsion only contains O(3)-symmetric tensor part according to irreducible decomposition. Some properties of the new solution are discussed.     

A comment on Kerr–CFT and Wald entropy

We point out that the entropies of black holes in general diffeomorphism invariant theories, computed using the Kerr–CFT correspondence and the Wald formula (as implemented in the entropy function formalism), need not always agree. A simple way to illustrate this is to consider Einstein–Gauss–Bonnet gravity in four dimensions, where the Gauss–Bonnet term is topological. This means that the central charge of Kerr–CFT computed in the Barnich–Brandt–Compere formalism remains the same as in Einstein gravity, while the entropy computed using the entropy function gives a universal correction proportional to the Gauss–Bonnet coupling. We argue that at least in this example, the Kerr–CFT result is the physically reasonable one. The resolution to this discrepancy might lie in a better understanding of boundary terms.     

Strings in strongly correlated electron systems

It is shown that strongly correlated electrons on frustrated lattices like pyrochlore, checkerboard or kagomè lattice can lead to the appearance of closed and open strings. They are resulting from nonlocal subsidiary conditions which propagating strongly correlated electrons require. The dynamics of the strings is discussed and a number of their properties are pointed out. Some of them are reminiscent of particle physics.     

Protein folding simulations in a deformed energy landscape

A modified version of stochastic tunneling, a recently introduced global optimization technique, is introduced as a new generalized-ensemble technique and tested for a benchmark peptide, Met-enkephalin. It is demonstrated that the new technique allows to evaluate folding properties and especially the glass temperature of this peptide. Received 2 September 1999     

Anomalies and de Sitter radiation from the generic black holes in de Sitter spaces

Robinson–Wilczek's recent work shows that, the energy–momentum tensor flux required to cancel gravitational anomaly at the event horizon of a Schwarzschild-type black hole has an equivalent form to that of a (1+1)$(1+1)$-dimensional blackbody radiation at the Hawking temperature. Motivated by their work, Hawking radiation from the cosmological horizons of the general Schwarzschild–de Sitter and Kerr–de Sitter black holes, has been studied by the method of anomaly cancellation. The result shows that the absorbing gauge current and energy momentum tensor fluxes required to cancel gauge and gravitational anomalies at the cosmological horizon are precisely equal to those of Hawking radiation from it. It should be emphasized that the effective field theory for generic black holes in de Sitter spaces should be formulated within the region between the event horizon (EH) and the cosmological horizon (CH), to integrate out the classically irrelevant ingoing modes at the EH and the classically irrelevant outgoing modes at the CH, respectively.     

Quantum Radiation of a Non-stationary Kerr-Newman Black Hole in de Sitter Space-Time

Hawking radiation of Klein-Gordon and Dirac particles in a non-stationary Kerr-Newman-de-Sitter black hole is studied by introducing a new tortoise coordinate transformation. The result shows that the Fermi-Dirac radiant spectrum displays a new term that represents the interaction between the spin of spinor particles and the rotation of black holes, which is absent in the Bose-Einstein distribution of Klein-Gordon particles.     

Massive Particles' de Sitter Tunneling in (3+1)-Dimensional de Sitter Spacetimes

In this paper, massive particles' Hawking radiation via tunneling from cosmological horizon of a (3+1)-dimensional de Sitter spacetime is investigated. According to Parikh's theory, when a particle tunnels across the cosmological horizon, the effective geometry is Schwarzschild-de Sitter spacetime. In this effective spacetime, a massive particle can be treated as a de Broglie S-wave. WKB method is used. The emission spectrum is obtained, and it takes the same functional form as that of massless particles.     

Cosmological Gravitational Wave in de Sitter Spacetime

Since there is always an incorrect sign in the mass of the graviton in the so-called perturbation expansion approximation of de Sitter spacetime, the existence of a gravitational wave from the metric perturbation of de Sitter spacetime is doubtful. We try to take another way to start from the assumption that the cosmological gravitation wave equation should be both general covariant and conformal invariant. It is found that the so-called conformal gravitation is no longer part of the metric field and it has an effective mass of mg=√R/6=√2A/3 with the correct sign in de Sitter spacetime, though its intrinsic mass remains zero.     

Accelerating black holes in anti-de Sitter universe

A physical interpretation of theC-metric with a negative cosmological constantΛ is suggested. Using a convenient coordinate system it is demonstrated that this class of exact solutions of Einstein’s equations describes uniformly accelerating (possibly charged) black holes in anti-de Sitter universe. Main differences from the analogous de Sitter case are emphasised. Dedicated to my academic teacher Prof. J. Bičák on the occasion of his 60th birthday. This work was supported by the grant GACR-202/99/0261 of the Czech Republic and GAUK 141/2000 of Charles University in Prague.